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Khair Muhammad Saraz

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These are questions asked by Khair Muhammad Saraz

How to assign values to u[i] so that it ...

Khair Muhammad Saraz 40 Maple
assign loop duplicate-question
August 09 2024
1 1

i am writing the code and unfortunately i am struck in a pb  where i assign initial condition values to u[i] from i 1 to N but when i use them in a loop it is not taking values of u[i] it is just taking value of u[1] only kindly help me in this regard i am attaching my file here.

automatic_differentiation.mw
 

> 

restart
> 

v := 1; a := 2; t := 0.1e-2; dt := 0.1e-3; N := 40; h := 1/40; K := 4
> 

NULL
> 

NULL
> 

for i from 0 to N do x[i] := i*h end do
> 

x[5]

1/8

 (1)
> 

initial_condition := []; for i to N do initial_condition := [op(initial_condition), evalf(2*v*Pi*sin(Pi*x[i])/(a+cos(Pi*x[i])))] end do
> 

initial_conditions := [.1644933719, .3289856976, .4934717144, .6579375992, .8223563570, .9866828090, 1.150848028, 1.314753051, 1.478261707, 1.641192349, 1.803308276, 1.964306617, 2.123805434, 2.281328760, 2.436289364, 2.587968970, 2.735495794, 2.877819368, 3.013682762, 3.141592654, 3.259788188, 3.366210070, 3.458472370, 3.533840560, 3.589220824, 3.621167336, 3.625916040, 3.599455182, 3.537643690, 3.436388151, 3.291886154, 3.100937330, 2.861312732, 2.572157998, 2.234388242, 1.851015873, 1.427342882, .9709526944, .4914580366, 0.]; u := proc (i) local u_x, u_xx, expr, j; u_x := (1/2)*(u[i+1]-u[i-1])/h; u_xx := (u[i-1]-2*u[i]+u[i+1])/h^2; expr := -alpha*u[i]*u_x+v*u_xx; expr end proc
NULL
> 

NULL
> 

odes := [seq(u(i, [seq(u[j], j = 1 .. N-1)]), i = 1 .. N-1)]
> 

for i to N-1 do assign(o[i] = odes[i]) end do
> 

for i to N-1 do printf("u_%d = %s\n", i, convert(u(i), string)) end do

u_1 = -alpha*u[1]*(20*u[2]-20*u[0])+1600*u[0]-3200*u[1]+1600*u[2]
u_2 = -alpha*u[2]*(20*u[3]-20*u[1])+1600*u[1]-3200*u[2]+1600*u[3]
u_3 = -alpha*u[3]*(20*u[4]-20*u[2])+1600*u[2]-3200*u[3]+1600*u[4]
u_4 = -alpha*u[4]*(20*u[5]-20*u[3])+1600*u[3]-3200*u[4]+1600*u[5]
u_5 = -alpha*u[5]*(20*u[6]-20*u[4])+1600*u[4]-3200*u[5]+1600*u[6]
u_6 = -alpha*u[6]*(20*u[7]-20*u[5])+1600*u[5]-3200*u[6]+1600*u[7]
u_7 = -alpha*u[7]*(20*u[8]-20*u[6])+1600*u[6]-3200*u[7]+1600*u[8]
u_8 = -alpha*u[8]*(20*u[9]-20*u[7])+1600*u[7]-3200*u[8]+1600*u[9]
u_9 = -alpha*u[9]*(20*u[10]-20*u[8])+1600*u[8]-3200*u[9]+1600*u[10]
u_10 = -alpha*u[10]*(20*u[11]-20*u[9])+1600*u[9]-3200*u[10]+1600*u[11]
u_11 = -alpha*u[11]*(20*u[12]-20*u[10])+1600*u[10]-3200*u[11]+1600*u[12]
u_12 = -alpha*u[12]*(20*u[13]-20*u[11])+1600*u[11]-3200*u[12]+1600*u[13]
u_13 = -alpha*u[13]*(20*u[14]-20*u[12])+1600*u[12]-3200*u[13]+1600*u[14]
u_14 = -alpha*u[14]*(20*u[15]-20*u[13])+1600*u[13]-3200*u[14]+1600*u[15]
u_15 = -alpha*u[15]*(20*u[16]-20*u[14])+1600*u[14]-3200*u[15]+1600*u[16]
u_16 = -alpha*u[16]*(20*u[17]-20*u[15])+1600*u[15]-3200*u[16]+1600*u[17]
u_17 = -alpha*u[17]*(20*u[18]-20*u[16])+1600*u[16]-3200*u[17]+1600*u[18]
u_18 = -alpha*u[18]*(20*u[19]-20*u[17])+1600*u[17]-3200*u[18]+1600*u[19]
u_19 = -alpha*u[19]*(20*u[20]-20*u[18])+1600*u[18]-3200*u[19]+1600*u[20]
u_20 = -alpha*u[20]*(20*u[21]-20*u[19])+1600*u[19]-3200*u[20]+1600*u[21]
u_21 = -alpha*u[21]*(20*u[22]-20*u[20])+1600*u[20]-3200*u[21]+1600*u[22]
u_22 = -alpha*u[22]*(20*u[23]-20*u[21])+1600*u[21]-3200*u[22]+1600*u[23]
u_23 = -alpha*u[23]*(20*u[24]-20*u[22])+1600*u[22]-3200*u[23]+1600*u[24]
u_24 = -alpha*u[24]*(20*u[25]-20*u[23])+1600*u[23]-3200*u[24]+1600*u[25]
u_25 = -alpha*u[25]*(20*u[26]-20*u[24])+1600*u[24]-3200*u[25]+1600*u[26]
u_26 = -alpha*u[26]*(20*u[27]-20*u[25])+1600*u[25]-3200*u[26]+1600*u[27]
u_27 = -alpha*u[27]*(20*u[28]-20*u[26])+1600*u[26]-3200*u[27]+1600*u[28]
u_28 = -alpha*u[28]*(20*u[29]-20*u[27])+1600*u[27]-3200*u[28]+1600*u[29]
u_29 = -alpha*u[29]*(20*u[30]-20*u[28])+1600*u[28]-3200*u[29]+1600*u[30]
u_30 = -alpha*u[30]*(20*u[31]-20*u[29])+1600*u[29]-3200*u[30]+1600*u[31]
u_31 = -alpha*u[31]*(20*u[32]-20*u[30])+1600*u[30]-3200*u[31]+1600*u[32]
u_32 = -alpha*u[32]*(20*u[33]-20*u[31])+1600*u[31]-3200*u[32]+1600*u[33]
u_33 = -alpha*u[33]*(20*u[34]-20*u[32])+1600*u[32]-3200*u[33]+1600*u[34]
u_34 = -alpha*u[34]*(20*u[35]-20*u[33])+1600*u[33]-3200*u[34]+1600*u[35]
u_35 = -alpha*u[35]*(20*u[36]-20*u[34])+1600*u[34]-3200*u[35]+1600*u[36]
u_36 = -alpha*u[36]*(20*u[37]-20*u[35])+1600*u[35]-3200*u[36]+1600*u[37]
u_37 = -alpha*u[37]*(20*u[38]-20*u[36])+1600*u[36]-3200*u[37]+1600*u[38]
u_38 = -alpha*u[38]*(20*u[39]-20*u[37])+1600*u[37]-3200*u[38]+1600*u[39]
u_39 = -alpha*u[39]*(20*u[40]-20*u[38])+1600*u[38]-3200*u[39]+1600*u[40]

  
> 

u := table(); for i to N do u[i] := initial_conditions[i] end do

.1644933719

  

.3289856976

  

.4934717144

  

.6579375992

  

.8223563570

  

.9866828090

  

1.150848028

  

1.314753051

  

1.478261707

  

1.641192349

  

1.803308276

  

1.964306617

  

2.123805434

  

2.281328760

  

2.436289364

  

2.587968970

  

2.735495794

  

2.877819368

  

3.013682762

  

3.141592654

  

3.259788188

  

3.366210070

  

3.458472370

  

3.533840560

  

3.589220824

  

3.621167336

  

3.625916040

  

3.599455182

  

3.537643690

  

3.436388151

  

3.291886154

  

3.100937330

  

2.861312732

  

2.572157998

  

2.234388242

  

1.851015873

  

1.427342882

  

.9709526944

  

.4914580366

  

0.

 (2)
> 

for i from 2 to N do T1[i] := (u[i+1]-u[i-1])/(2*h); T2[i] := u[i]*T1[i]; T3[i] := (u[i-1]-2*u[i]+u[i+1])/h^2; u[i][1] := v*T3[i]-T2[i] end do

20*u[3]-3.289867438

  

u[2]*(20*u[3]-3.289867438)

  

263.1893950-3200*u[2]+1600*u[3]

  

263.1893950-3200*u[2]+1600*u[3]-u[2]*(20*u[3]-3.289867438)

  

20*u[4]-20*u[2]

  

u[3]*(20*u[4]-20*u[2])

  

1600*u[2]-3200*u[3]+1600*u[4]

  

1600*u[2]-3200*u[3]+1600*u[4]-u[3]*(20*u[4]-20*u[2])

  

20*u[5]-20*u[3]

  

u[4]*(20*u[5]-20*u[3])

  

1600*u[3]-3200*u[4]+1600*u[5]

  

1600*u[3]-3200*u[4]+1600*u[5]-u[4]*(20*u[5]-20*u[3])

  

20*u[6]-20*u[4]

  

u[5]*(20*u[6]-20*u[4])

  

1600*u[4]-3200*u[5]+1600*u[6]

  

1600*u[4]-3200*u[5]+1600*u[6]-u[5]*(20*u[6]-20*u[4])

  

20*u[7]-20*u[5]

  

u[6]*(20*u[7]-20*u[5])

  

1600*u[5]-3200*u[6]+1600*u[7]

  

1600*u[5]-3200*u[6]+1600*u[7]-u[6]*(20*u[7]-20*u[5])

  

20*u[8]-20*u[6]

  

u[7]*(20*u[8]-20*u[6])

  

1600*u[6]-3200*u[7]+1600*u[8]

  

1600*u[6]-3200*u[7]+1600*u[8]-u[7]*(20*u[8]-20*u[6])

  

20*u[9]-20*u[7]

  

u[8]*(20*u[9]-20*u[7])

  

1600*u[7]-3200*u[8]+1600*u[9]

  

1600*u[7]-3200*u[8]+1600*u[9]-u[8]*(20*u[9]-20*u[7])

  

20*u[10]-20*u[8]

  

u[9]*(20*u[10]-20*u[8])

  

1600*u[8]-3200*u[9]+1600*u[10]

  

1600*u[8]-3200*u[9]+1600*u[10]-u[9]*(20*u[10]-20*u[8])

  

20*u[11]-20*u[9]

  

u[10]*(20*u[11]-20*u[9])

  

1600*u[9]-3200*u[10]+1600*u[11]

  

1600*u[9]-3200*u[10]+1600*u[11]-u[10]*(20*u[11]-20*u[9])

  

20*u[12]-20*u[10]

  

u[11]*(20*u[12]-20*u[10])

  

1600*u[10]-3200*u[11]+1600*u[12]

  

1600*u[10]-3200*u[11]+1600*u[12]-u[11]*(20*u[12]-20*u[10])

  

20*u[13]-20*u[11]

  

u[12]*(20*u[13]-20*u[11])

  

1600*u[11]-3200*u[12]+1600*u[13]

  

1600*u[11]-3200*u[12]+1600*u[13]-u[12]*(20*u[13]-20*u[11])

  

20*u[14]-20*u[12]

  

u[13]*(20*u[14]-20*u[12])

  

1600*u[12]-3200*u[13]+1600*u[14]

  

1600*u[12]-3200*u[13]+1600*u[14]-u[13]*(20*u[14]-20*u[12])

  

20*u[15]-20*u[13]

  

u[14]*(20*u[15]-20*u[13])

  

1600*u[13]-3200*u[14]+1600*u[15]

  

1600*u[13]-3200*u[14]+1600*u[15]-u[14]*(20*u[15]-20*u[13])

  

20*u[16]-20*u[14]

  

u[15]*(20*u[16]-20*u[14])

  

1600*u[14]-3200*u[15]+1600*u[16]

  

1600*u[14]-3200*u[15]+1600*u[16]-u[15]*(20*u[16]-20*u[14])

  

20*u[17]-20*u[15]

  

u[16]*(20*u[17]-20*u[15])

  

1600*u[15]-3200*u[16]+1600*u[17]

  

1600*u[15]-3200*u[16]+1600*u[17]-u[16]*(20*u[17]-20*u[15])

  

20*u[18]-20*u[16]

  

u[17]*(20*u[18]-20*u[16])

  

1600*u[16]-3200*u[17]+1600*u[18]

  

1600*u[16]-3200*u[17]+1600*u[18]-u[17]*(20*u[18]-20*u[16])

  

20*u[19]-20*u[17]

  

u[18]*(20*u[19]-20*u[17])

  

1600*u[17]-3200*u[18]+1600*u[19]

  

1600*u[17]-3200*u[18]+1600*u[19]-u[18]*(20*u[19]-20*u[17])

  

20*u[20]-20*u[18]

  

u[19]*(20*u[20]-20*u[18])

  

1600*u[18]-3200*u[19]+1600*u[20]

  

1600*u[18]-3200*u[19]+1600*u[20]-u[19]*(20*u[20]-20*u[18])

  

20*u[21]-20*u[19]

  

u[20]*(20*u[21]-20*u[19])

  

1600*u[19]-3200*u[20]+1600*u[21]

  

1600*u[19]-3200*u[20]+1600*u[21]-u[20]*(20*u[21]-20*u[19])

  

20*u[22]-20*u[20]

  

u[21]*(20*u[22]-20*u[20])

  

1600*u[20]-3200*u[21]+1600*u[22]

  

1600*u[20]-3200*u[21]+1600*u[22]-u[21]*(20*u[22]-20*u[20])

  

20*u[23]-20*u[21]

  

u[22]*(20*u[23]-20*u[21])

  

1600*u[21]-3200*u[22]+1600*u[23]

  

1600*u[21]-3200*u[22]+1600*u[23]-u[22]*(20*u[23]-20*u[21])

  

20*u[24]-20*u[22]

  

u[23]*(20*u[24]-20*u[22])

  

1600*u[22]-3200*u[23]+1600*u[24]

  

1600*u[22]-3200*u[23]+1600*u[24]-u[23]*(20*u[24]-20*u[22])

  

20*u[25]-20*u[23]

  

u[24]*(20*u[25]-20*u[23])

  

1600*u[23]-3200*u[24]+1600*u[25]

  

1600*u[23]-3200*u[24]+1600*u[25]-u[24]*(20*u[25]-20*u[23])

  

20*u[26]-20*u[24]

  

u[25]*(20*u[26]-20*u[24])

  

1600*u[24]-3200*u[25]+1600*u[26]

  

1600*u[24]-3200*u[25]+1600*u[26]-u[25]*(20*u[26]-20*u[24])

  

20*u[27]-20*u[25]

  

u[26]*(20*u[27]-20*u[25])

  

1600*u[25]-3200*u[26]+1600*u[27]

  

1600*u[25]-3200*u[26]+1600*u[27]-u[26]*(20*u[27]-20*u[25])

  

20*u[28]-20*u[26]

  

u[27]*(20*u[28]-20*u[26])

  

1600*u[26]-3200*u[27]+1600*u[28]

  

1600*u[26]-3200*u[27]+1600*u[28]-u[27]*(20*u[28]-20*u[26])

  

20*u[29]-20*u[27]

  

u[28]*(20*u[29]-20*u[27])

  

1600*u[27]-3200*u[28]+1600*u[29]

  

1600*u[27]-3200*u[28]+1600*u[29]-u[28]*(20*u[29]-20*u[27])

  

20*u[30]-20*u[28]

  

u[29]*(20*u[30]-20*u[28])

  

1600*u[28]-3200*u[29]+1600*u[30]

  

1600*u[28]-3200*u[29]+1600*u[30]-u[29]*(20*u[30]-20*u[28])

  

20*u[31]-20*u[29]

  

u[30]*(20*u[31]-20*u[29])

  

1600*u[29]-3200*u[30]+1600*u[31]

  

1600*u[29]-3200*u[30]+1600*u[31]-u[30]*(20*u[31]-20*u[29])

  

20*u[32]-20*u[30]

  

u[31]*(20*u[32]-20*u[30])

  

1600*u[30]-3200*u[31]+1600*u[32]

  

1600*u[30]-3200*u[31]+1600*u[32]-u[31]*(20*u[32]-20*u[30])

  

20*u[33]-20*u[31]

  

u[32]*(20*u[33]-20*u[31])

  

1600*u[31]-3200*u[32]+1600*u[33]

  

1600*u[31]-3200*u[32]+1600*u[33]-u[32]*(20*u[33]-20*u[31])

  

20*u[34]-20*u[32]

  

u[33]*(20*u[34]-20*u[32])

  

1600*u[32]-3200*u[33]+1600*u[34]

  

1600*u[32]-3200*u[33]+1600*u[34]-u[33]*(20*u[34]-20*u[32])

  

20*u[35]-20*u[33]

  

u[34]*(20*u[35]-20*u[33])

  

1600*u[33]-3200*u[34]+1600*u[35]

  

1600*u[33]-3200*u[34]+1600*u[35]-u[34]*(20*u[35]-20*u[33])

  

20*u[36]-20*u[34]

  

u[35]*(20*u[36]-20*u[34])

  

1600*u[34]-3200*u[35]+1600*u[36]

  

1600*u[34]-3200*u[35]+1600*u[36]-u[35]*(20*u[36]-20*u[34])

  

20*u[37]-20*u[35]

  

u[36]*(20*u[37]-20*u[35])

  

1600*u[35]-3200*u[36]+1600*u[37]

  

1600*u[35]-3200*u[36]+1600*u[37]-u[36]*(20*u[37]-20*u[35])

  

20*u[38]-20*u[36]

  

u[37]*(20*u[38]-20*u[36])

  

1600*u[36]-3200*u[37]+1600*u[38]

  

1600*u[36]-3200*u[37]+1600*u[38]-u[37]*(20*u[38]-20*u[36])

  

20*u[39]-20*u[37]

  

u[38]*(20*u[39]-20*u[37])

  

1600*u[37]-3200*u[38]+1600*u[39]

  

1600*u[37]-3200*u[38]+1600*u[39]-u[38]*(20*u[39]-20*u[37])

  

20*u[40]-20*u[38]

  

u[39]*(20*u[40]-20*u[38])

  

1600*u[38]-3200*u[39]+1600*u[40]

  

1600*u[38]-3200*u[39]+1600*u[40]-u[39]*(20*u[40]-20*u[38])

  

20*u[41]-20*u[39]

  

u[40]*(20*u[41]-20*u[39])

  

1600*u[39]-3200*u[40]+1600*u[41]

  

1600*u[39]-3200*u[40]+1600*u[41]-u[40]*(20*u[41]-20*u[39])

 (3)
> 

u[1]

.1644933719

 (4)
> 

u[2]

u[2]

 (5)
 

NULL

Download automatic_differentiation.mw

How do i resolve my code which encounter...

Khair Muhammad Saraz 40 Maple
differentiation
August 07 2024
1 1

i am trying to make code for automatic differentiation method. kindly help me out with that. i have asked chatgpt too. i am going to attach my file alongwith chatgpt code kindly help meautomatic_differentiation.mw
 

> 

restart
> 

v := 1; a := 2; t := 0.1e-2; dt := 0.1e-3; N := 40; h := 1/40; K := 4
> 

NULL
> 

NULL
> 

for i from 0 to N do x[i] := i*h end do
> 

NULL
> 

initial_conditions := []; for i to N do initial_conditions := [op(initial_conditions), 2*v*Pi*sin(Pi*x[i])/(a+cos(Pi*x[i]))] end do
> 

u := proc (i) local u_x, u_xx, expr, j; u_x := (1/2)*(u[i+1]-u[i-1])/h; u_xx := (u[i-1]-2*u[i]+u[i+1])/h^2; expr := -alpha*u[i]*u_x+v*u_xx; expr end proc
NULL
> 

NULL
> 

odes := [seq(u(i, [seq(u[j], j = 1 .. N-1)]), i = 1 .. N-1)]
> 

for i to N-1 do assign(o[i] = odes[i]) end do
> 

for i to N-1 do printf("u_%d = %s\n", i, convert(u(i), string)) end do

u_1 = -alpha*u[1]*(20*u[2]-20*u[0])+1600*u[0]-3200*u[1]+1600*u[2]
u_2 = -alpha*u[2]*(20*u[3]-20*u[1])+1600*u[1]-3200*u[2]+1600*u[3]
u_3 = -alpha*u[3]*(20*u[4]-20*u[2])+1600*u[2]-3200*u[3]+1600*u[4]
u_4 = -alpha*u[4]*(20*u[5]-20*u[3])+1600*u[3]-3200*u[4]+1600*u[5]
u_5 = -alpha*u[5]*(20*u[6]-20*u[4])+1600*u[4]-3200*u[5]+1600*u[6]
u_6 = -alpha*u[6]*(20*u[7]-20*u[5])+1600*u[5]-3200*u[6]+1600*u[7]
u_7 = -alpha*u[7]*(20*u[8]-20*u[6])+1600*u[6]-3200*u[7]+1600*u[8]
u_8 = -alpha*u[8]*(20*u[9]-20*u[7])+1600*u[7]-3200*u[8]+1600*u[9]
u_9 = -alpha*u[9]*(20*u[10]-20*u[8])+1600*u[8]-3200*u[9]+1600*u[10]
u_10 = -alpha*u[10]*(20*u[11]-20*u[9])+1600*u[9]-3200*u[10]+1600*u[11]
u_11 = -alpha*u[11]*(20*u[12]-20*u[10])+1600*u[10]-3200*u[11]+1600*u[12]
u_12 = -alpha*u[12]*(20*u[13]-20*u[11])+1600*u[11]-3200*u[12]+1600*u[13]
u_13 = -alpha*u[13]*(20*u[14]-20*u[12])+1600*u[12]-3200*u[13]+1600*u[14]
u_14 = -alpha*u[14]*(20*u[15]-20*u[13])+1600*u[13]-3200*u[14]+1600*u[15]
u_15 = -alpha*u[15]*(20*u[16]-20*u[14])+1600*u[14]-3200*u[15]+1600*u[16]
u_16 = -alpha*u[16]*(20*u[17]-20*u[15])+1600*u[15]-3200*u[16]+1600*u[17]
u_17 = -alpha*u[17]*(20*u[18]-20*u[16])+1600*u[16]-3200*u[17]+1600*u[18]
u_18 = -alpha*u[18]*(20*u[19]-20*u[17])+1600*u[17]-3200*u[18]+1600*u[19]
u_19 = -alpha*u[19]*(20*u[20]-20*u[18])+1600*u[18]-3200*u[19]+1600*u[20]
u_20 = -alpha*u[20]*(20*u[21]-20*u[19])+1600*u[19]-3200*u[20]+1600*u[21]
u_21 = -alpha*u[21]*(20*u[22]-20*u[20])+1600*u[20]-3200*u[21]+1600*u[22]
u_22 = -alpha*u[22]*(20*u[23]-20*u[21])+1600*u[21]-3200*u[22]+1600*u[23]
u_23 = -alpha*u[23]*(20*u[24]-20*u[22])+1600*u[22]-3200*u[23]+1600*u[24]
u_24 = -alpha*u[24]*(20*u[25]-20*u[23])+1600*u[23]-3200*u[24]+1600*u[25]
u_25 = -alpha*u[25]*(20*u[26]-20*u[24])+1600*u[24]-3200*u[25]+1600*u[26]
u_26 = -alpha*u[26]*(20*u[27]-20*u[25])+1600*u[25]-3200*u[26]+1600*u[27]
u_27 = -alpha*u[27]*(20*u[28]-20*u[26])+1600*u[26]-3200*u[27]+1600*u[28]
u_28 = -alpha*u[28]*(20*u[29]-20*u[27])+1600*u[27]-3200*u[28]+1600*u[29]
u_29 = -alpha*u[29]*(20*u[30]-20*u[28])+1600*u[28]-3200*u[29]+1600*u[30]
u_30 = -alpha*u[30]*(20*u[31]-20*u[29])+1600*u[29]-3200*u[30]+1600*u[31]
u_31 = -alpha*u[31]*(20*u[32]-20*u[30])+1600*u[30]-3200*u[31]+1600*u[32]
u_32 = -alpha*u[32]*(20*u[33]-20*u[31])+1600*u[31]-3200*u[32]+1600*u[33]
u_33 = -alpha*u[33]*(20*u[34]-20*u[32])+1600*u[32]-3200*u[33]+1600*u[34]
u_34 = -alpha*u[34]*(20*u[35]-20*u[33])+1600*u[33]-3200*u[34]+1600*u[35]
u_35 = -alpha*u[35]*(20*u[36]-20*u[34])+1600*u[34]-3200*u[35]+1600*u[36]
u_36 = -alpha*u[36]*(20*u[37]-20*u[35])+1600*u[35]-3200*u[36]+1600*u[37]
u_37 = -alpha*u[37]*(20*u[38]-20*u[36])+1600*u[36]-3200*u[37]+1600*u[38]
u_38 = -alpha*u[38]*(20*u[39]-20*u[37])+1600*u[37]-3200*u[38]+1600*u[39]
u_39 = -alpha*u[39]*(20*u[40]-20*u[38])+1600*u[38]-3200*u[39]+1600*u[40]

  
> 

eval_derivatives := proc (k, u) local T1i, T2i, T3i, T1ik, T2ik, T3ik, ui_k, i, j; T1i := Array(0 .. N); T2i := Array(0 .. N); T3i := Array(0 .. N); ui_k := Array(0 .. N); for i to N-1 do T1i[i] := (1/2)*(u[i+1]-u[i-1])/h; T2i[i] := u[i]*T1i[i]; T3i[i] := (u[i-1]-2*u[i]+u[i+1])/h^2; ui_k[i] := v*T3i[i]-T2i[i] end do; T1ik := Array(0 .. N); T2ik := Array(0 .. N); T3ik := Array(0 .. N); for i to N-1 do T1ik[i] := (1/2)*(u[i+1, k]-u[i-1, k])/h; T2ik[i] := add(u[i, j]*T1i[i, k-j], j = 0 .. k); T3ik[i] := (u[i-1, k]-2*u[i, k]+u[i+1, k])/h^2; ui_k[i] := (v*T3ik[i]-T2ik[i])/(k+1) end do; return ui_k end proc
``

proc (k, u) local T1i, T2i, T3i, T1ik, T2ik, T3ik, ui_k, i, j; T1i := Array(0 .. N); T2i := Array(0 .. N); T3i := Array(0 .. N); ui_k := Array(0 .. N); for i to N-1 do T1i[i] := (1/2)*(u[i+1]-u[i-1])/h; T2i[i] := u[i]*T1i[i]; T3i[i] := (u[i-1]-2*u[i]+u[i+1])/h^2; ui_k[i] := v*T3i[i]-T2i[i] end do; T1ik := Array(0 .. N); T2ik := Array(0 .. N); T3ik := Array(0 .. N); for i to N-1 do T1ik[i] := (1/2)*(u[i+1, k]-u[i-1, k])/h; T2ik[i] := add(u[i, j]*T1i[i, k-j], j = 0 .. k); T3ik[i] := (u[i-1, k]-2*u[i, k]+u[i+1, k])/h^2; ui_k[i] := (v*T3ik[i]-T2ik[i])/(k+1) end do; return ui_k end proc

 (1)
> 

u := Array(1 .. N, 0 .. K); for i to N do u[i, 0] := evalf(initial_conditions[i]) end do

Array(%id = 36893489585014251020)

  

.1644933719

  

.3289856976

  

.4934717144

  

.6579375992

  

.8223563570

  

.9866828090

  

1.150848028

  

1.314753051

  

1.478261707

  

1.641192349

  

1.803308276

  

1.964306617

  

2.123805434

  

2.281328760

  

2.436289364

  

2.587968970

  

2.735495794

  

2.877819368

  

3.013682762

  

3.141592654

  

3.259788188

  

3.366210070

  

3.458472370

  

3.533840560

  

3.589220824

  

3.621167336

  

3.625916040

  

3.599455182

  

3.537643690

  

3.436388151

  

3.291886154

  

3.100937330

  

2.861312732

  

2.572157998

  

2.234388242

  

1.851015873

  

1.427342882

  

.9709526944

  

.4914580366

  

0.

 (2)
> 

for k to K do ui_k := eval_derivatives(k, u); for i to N-1 do u[i, k] := ui_k[i] end do end do

Error, (in eval_derivatives) Array index out of range

  
> 

NULL
> 

" local u_new, i, k; u_new := Array(1..N); for i from 1 to N do u_new[i] := evalf(add(u[i, k] * dt^k / factorial(k), k = 0 .. K)); end do; return u_new; end proc;"

Error, unable to parse

" local u_new, i, k; u_new := Array(1..N); for i from 1 to N do u_new[i] := evalf(add(u[i, k] * dt^k / factorial(k), k = 0 .. K)); end do; return u_new; end proc;"

  
> 

num_steps := round(0.1e-2/dt); for step to num_steps do u_new := advance_solution(t, dt, K, u); for i to N do u[i, 0] := u_new[i] end do; for k to K do ui_k := eval_derivatives(k, u); for i to N do u[i, k] := ui_k[i] end do end do; t := t+dt end do; print(u_new)

num_steps := 10

  

advance_solution(0.1e-2, 0.1e-3, 4, Array(%id = 36893489585014251020))

 (3)
> 

NULL


 

Download automatic_differentiation.mw

resolve the issue

How to evaluate definite integral withou...

Khair Muhammad Saraz 40 Maple
integration
August 02 2024
1 1

i am trying to solve definite integral but i want result in A,B form i dont want to assign numerical values to them can i get that  in maple? i have tried evalf, eval and simplify command but it is not working kindly help me out

> 

restart
> 

NULL
> 

integrand := p*exp(-A/sqrt(p)-B/p)

p*exp(-A/p^(1/2)-B/p)

 (1)
> 

integral := int(integrand, p = 0 .. infinity)

int(p*exp(-A/p^(1/2)-B/p), p = 0 .. infinity)

 (2)
> 

simplify(integral)

int(p*exp(-(A*p+B*p^(1/2))/p^(3/2)), p = 0 .. infinity)

 (3)
> 

evalf(integral)

int(p*exp(-1.*A/p^(1/2)-1.*B/p), p = 0. .. Float(infinity))

 (4)
> 

eval(integral)

int(p*exp(-A/p^(1/2)-B/p), p = 0 .. infinity)

 (5)
 

NULL

Download integral.mwintegral.mw

why i am facing issues while changing th...

Khair Muhammad Saraz 40 Maple 2022
homework numeric differential-equations
July 04 2024
1 5

i have made a full working code for differential quadrature method now i am  changing examples and it is not working although i have properly defined new parameters i am attaching my code kindly help me out
one more thing one example include summation n=0..ininity it is not even evaluating taking alot of time i am attaching both codes kindly help me out
A+B_example.mw
chelishkov_comparison.mw

How do i re-edit my maple file after eva...

Khair Muhammad Saraz 40 Maple 2022
worksheet pde differential-equations
June 29 2024
1 5

while running my code i am not able to edit it. when i close my file and re open it then it is edit able but only once after that to re edit i have to run it again.
one more query i am facing is that i have made whole code now i just want to change pde and exact solution of that pde to get different solutions of pde although my code is working for one pde but while changing pde it is giving me error why?
and some times it takes alot of time to evaluate is there any error in the code or should i change my laptop?

kindly help me with all these queries.

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