666 jvbasha

javid basha jv

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These are questions asked by 666 jvbasha

Dear maple users.

Greetings for the day.

I hope you are all fine and safe.

In the below mention code, I need to plot "ax" at 0..1 when N=1 and N=2.

But the code only working for the N=0 case.

How to tackle this situation and plot the function for various values of "ax" at ax=0..1.

waiting for your reply.

JBV.mw

Code:

restart;
PDEtools[declare](f(x), t(x), g(x), prime = (x));

N := 2; m := .2; pa := 3.14*(1/3); ax := ax; h2 := 1+.2*ax+.3*sin((2*3.14)*(ax-.2)); h1 := -1-.2*ax-.1*sin((2*3.14)*(ax-.2)+pa); a2 := 1.4+.1*sin((2*3.14)*(ax-.2))+.3*sin((2*3.14)*(ax-.2)+pa);

f(x):=sum(p^j*f[j](x),j=0..N);  t(x):=sum(p^j*t[j](x),j=0..N);

g(x):=sum(p^j*g[j](x),j=0..N);

Eq1 := (1-p)*(diff(f(x), `$`(x, 4)))+p*((1+.2)*(diff(f(x), `$`(x, 4)))-(.2*(1/3))*(diff((diff(f(x), `$`(x, 2)))^3, `$`(x, 2)))-2*(diff(f(x), `$`(x, 2)))+diff(t(x), `$`(x, 1))+diff(g(x), `$`(x, 1)));

Eq2 := (1-p)*(1+1.2)*(diff(t(x), `$`(x, 2)))+p*((1+1.2)*(diff(t(x), `$`(x, 2)))+.1*(diff(t(x), `$`(x, 1)))*(diff(g(x), `$`(x, 1)))+.2*(diff(t(x), `$`(x, 1)))^2+.5*(diff(f(x), `$`(x, 1)))^2);

Eq3 := (1-p)*(diff(g(x), `$`(x, 2)))+p*(diff(g(x), `$`(x, 2))+diff(t(x), `$`(x, 2)));

for j from 0 to N do
equ1[j] := coeff(Eq1, p, j) = 0; 
equ2[j] := coeff(Eq2, p, j) = 0;
equ3[j] := coeff(Eq3, p, j) = 0;
end do;

con[1][0] := f[0](h2) = (1/2)*a2, (D(f[0]))(h2) = 0, f[0](h1) = -(1/2)*a2, (D(f[0]))(h1) = 0; con[2][0] := t[0](h2) = 1, t[0](h1) = 0; con[3][0] := g[0](h2) = 1, g[0](h1) = 0;

for i to N do

con[1][i] := f[i](h2) = 0, (D(f[i]))(h2) = 0, f[i](h1) = 0, (D(f[i]))(h1) = 0; con[2][i] := t[i](h2) = 0, t[i](h1) = 0; con[3][i] := g[i](h2) = 0, g[i](h1) = 0 end do;

for i from 0 to N do
P:=dsolve({equ1[i],equ2[i],equ3[i],con[1][i],con[2][i],con[3][i]},{f[i](x),t[i](x),g[i](x)}):
f[i](x):=rhs(P[1]);
t[i](x):=rhs(P[2]);
g[i](x):=rhs(P[3]);
end do:

f(x):=evalf(simplify(sum(f[n](x),n=0..N)));
Am := (1+.2)*(diff(f(x), `$`(x, 3)));
with(plots);

display(plot(eval(Am, x = .6), ax = 0 .. 1, numpoints = 200, color = blue));
 

Dear maple users,

Greetings.

When converting the maple figure into EPS format (for latex) which shows white patches.

How to avoid such patches.

Dear maple users,

Greetings.


JVB.mw
 

restart; with(plots)

fcns := {f(x), g(x), t(x)}

m := .2; pa := 3.14*(1/3); aa := .1; bb := .3; ta := .2; kt := .4; h2 := 1+m*ax+bb*sin((2*3.14)*(ax-ta)); h1 := -1-m*ax-aa*sin((2*3.14)*(ax-ta)+pa); a2 := kt+aa*sin((2*3.14)*(ax-ta))+bb*sin((2*3.14)*(ax-ta)+pa)

1+.2*ax+.3*sin(6.28*ax-1.256)

 

-1-.2*ax-.1*sin(6.28*ax-.209333333)

 

.4+.1*sin(6.28*ax-1.256)+.3*sin(6.28*ax-.209333333)

(1)

eq1 := 1.5*(diff(f(x), `$`(x, 4)))-.40*(diff((diff(f(x), `$`(x, 2)))^3, `$`(x, 2)))-.20*(diff(f(x), `$`(x, 2)))+.20*(diff(t(x), `$`(x, 1)))+.20*(diff(g(x), `$`(x, 1))) = 0

1.5*(diff(diff(diff(diff(f(x), x), x), x), x))-2.40*(diff(diff(f(x), x), x))*(diff(diff(diff(f(x), x), x), x))^2-1.20*(diff(diff(f(x), x), x))^2*(diff(diff(diff(diff(f(x), x), x), x), x))-.20*(diff(diff(f(x), x), x))+.20*(diff(t(x), x))+.20*(diff(g(x), x)) = 0

(2)

eq2 := 1.75*(diff(t(x), `$`(x, 2)))+(diff(t(x), `$`(x, 1)))*(diff(g(x), `$`(x, 1)))+2*(diff(t(x), `$`(x, 1)))^2+.7*((diff(f(x), `$`(x, 2)))^2-(diff(f(x), `$`(x, 2)))^4)+.1*(diff(f(x), `$`(x, 1)))^2+.1*t(x) = 0

1.75*(diff(diff(t(x), x), x))+(diff(t(x), x))*(diff(g(x), x))+2*(diff(t(x), x))^2+.7*(diff(diff(f(x), x), x))^2-.7*(diff(diff(f(x), x), x))^4+.1*(diff(f(x), x))^2+.1*t(x) = 0

(3)

eq3 := diff(g(x), `$`(x, 2))+2*(diff(t(x), `$`(x, 2)))-.5*g(x) = 0

diff(diff(g(x), x), x)+2*(diff(diff(t(x), x), x))-.5*g(x) = 0

(4)

bc := f(h2) = (1/2)*a2, (D(f))(h2) = 0, f(h1) = -(1/2)*a2, (D(f))(h1) = 0, t(h2) = 1, t(h1) = 0, g(h2) = 1, g(h1) = 0

f(1+.2*ax+.3*sin(6.28*ax-1.256)) = .2000000000+0.5000000000e-1*sin(6.28*ax-1.256)+.1500000000*sin(6.28*ax-.209333333), (D(f))(1+.2*ax+.3*sin(6.28*ax-1.256)) = 0, f(-1-.2*ax-.1*sin(6.28*ax-.209333333)) = -.2000000000-0.5000000000e-1*sin(6.28*ax-1.256)-.1500000000*sin(6.28*ax-.209333333), (D(f))(-1-.2*ax-.1*sin(6.28*ax-.209333333)) = 0, t(1+.2*ax+.3*sin(6.28*ax-1.256)) = 1, t(-1-.2*ax-.1*sin(6.28*ax-.209333333)) = 0, g(1+.2*ax+.3*sin(6.28*ax-1.256)) = 1, g(-1-.2*ax-.1*sin(6.28*ax-.209333333)) = 0

(5)

L := [.1]; AP := NULL; NN := nops(L); for k to NN do R := dsolve(eval({bc, eq1, eq2, eq3}, ax = L[k]), fcns, type = numeric, method = bvp[midrich], maxmesh = 1000, abserr = 10^(-4), AP); AP := approxsoln = R; X1 || k := rhs(R(0)[4]) end do; ba3 := [(X1 || (1 .. NN))(0)]

[.1]

 

1

 

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

 

R(0)

(6)

``


 

Download JVB.mw

 

How to obtain a solution for various values of "ax"

waiting for your reply.

 

 

Dear maple users @acer @Carl Love @Kitonum @Preben Alsholm @dharr @tomleslie

Greeting.

I have solved some PDEs in analytically and numerically.

But the numerical and analytical results are not matching.

I hope there is some problem with an analytical solution, especially in the first order and second-order boundary conditions.

Both the codes have enclosed here, waiting for a reply.

AN.mw

NUM.mw

Note: The PDEs are performed in the Maple 18 version. 

When compiling an analytical solution, in clarify expression click the remember table assignment.

 

Dear maple users,

Greetings.

Q1.How to plot a figure for different values of M?

      like M=1,2,3,4:

Code:Mplot.mw

Q2. How to assign all the expressions are "remember table assignment"

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