salim-barzani

solve equations with condition parameter...

Asked: salim-barzani 1785 Product: Maple 2021

July 30 2024

0 1

before run file remove all (:) i want calculate equation but with a condition for example: when a=4 then find other parameter in my equation with respect to a=4 find other

usesol.mw

How choose the case after finding parame...

Asked: salim-barzani 1785 Product: Maple 2021

July 28 2024

1 5

when i finding parameter i want just choose a case for example a_1=a_1 and any other case a_2=0,and remove other case how i can do in maple

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ode := F(xi)^5*a[4]+F(xi)^4*a[3]+F(xi)^3*a[2]+(-k^2*a[1]+(diff(diff(F(xi), xi), xi))*a[5]-w)*F(xi)^2+(1/2)*F(xi)*(diff(diff(F(xi), xi), xi))*a[1]-(1/4)*(diff(F(xi), xi))^2*a[1] = 0

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S := sum(A[i]*Q(xi)^i, i = 0 .. 1)+sum(B[i]*Q(xi)^(-i), i = 1 .. 1)

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Warning, computation interrupted

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Warning, solutions may have been lost

${k = k, w = w, A[0] = 0, A[1] = A[1], B[1] = 0, a[1] = a[1], a[2] = a[2], a[3] = a[3], a[4] = a[4], a[5] = a[5]}, {k = k, w = -4*A[0]*a[5], A[0] = A[0], A[1] = A[1], B[1] = B[1], a[1] = 0, a[2] = -4*a[5], a[3] = 0, a[4] = 0, a[5] = a[5]}, {k = k, w = (1/2)*A[0]*(3*k^2*A[0]^2*a[4]+2*k^2*A[0]*a[3]+k^2*a[2]+4*k^2*a[5]+2*A[0]^2*a[4]+2*A[0]*a[3]+2*a[2]), A[0] = A[0], A[1] = 0, B[1] = 0, a[1] = -(1/2)*A[0]*(3*A[0]^2*a[4]+2*A[0]*a[3]+a[2]+4*a[5]), a[2] = a[2], a[3] = a[3], a[4] = a[4], a[5] = a[5]}, {k = k, w = w, A[0] = A[0], A[1] = 0, B[1] = 0, a[1] = a[1], a[2] = (-A[0]^3*a[4]+k^2*a[1]-A[0]^2*a[3]+w)/A[0], a[3] = a[3], a[4] = a[4], a[5] = a[5]}, {k = k, w = 4*A[1]*a[5]+4*B[1]*a[5], A[0] = -A[1]-B[1], A[1] = A[1], B[1] = B[1], a[1] = 0, a[2] = -4*a[5], a[3] = 0, a[4] = 0, a[5] = a[5]}, {k = k, w = -k^2*a[1]-4*A[0]*a[5]+a[1], A[0] = A[0], A[1] = (1/4)*A[0]^2/B[1], B[1] = B[1], a[1] = a[1], a[2] = -4*a[5], a[3] = 0, a[4] = 0, a[5] = a[5]}, {k = k, w = w, A[0] = 2*B[1], A[1] = B[1], B[1] = B[1], a[1] = a[1], a[2] = (1/2)*(k^2*a[1]+w-a[1])/B[1], a[3] = 0, a[4] = 0, a[5] = -(1/8)*(k^2*a[1]+w-a[1])/B[1]}, {k = k, w = w, A[0] = A[0], A[1] = B[1], B[1] = B[1], a[1] = 0, a[2] = w/A[0], a[3] = 0, a[4] = 0, a[5] = -(1/4)*w/A[0]}, {k = k, w = 0, A[0] = 0, A[1] = B[1], B[1] = B[1], a[1] = 0, a[2] = a[2], a[3] = 0, a[4] = 0, a[5] = -(1/4)*a[2]}$

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Download choose_case.mw

simplify the multiply exponential term ...

Asked: salim-barzani 1785 Product: Maple 2021

July 28 2024

1 2

i am looking for simplify this type of simplifying assume beta is Real and there is any stuf package for working with complex and conjugate automaticaly

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(-2*beta^2*exp((2*I)*x)*conjugate(beta*exp(I*x))+(I*conjugate(beta*exp(I*x))+1+I)*(conjugate(beta*exp(I*x))+(-1+I))*exp((3*I)*x)*beta^3)/s

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Download simplify.mw

calculate adomian polynomial ...

Asked: salim-barzani 1785 Product: Maple 2021

July 25 2024

0 11

Hi
i write my code for calculate this type of function but the result is so different from mine i will post here i hope someone tell me where is problem

i have this

i want this

Download EX1.mw

How Making loop for collecting solution?...

Asked: salim-barzani 1785 Product: Maple 2021

July 24 2024

1 3

Hi
i did calculation part by part of adomian laplace method but if we can make a loop for it is gonna be so great and take back a lot of time

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pde := diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x)) = t^2*x+x

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s*laplace(u(x, t), t, s)-u(x, 0)+laplace(u(x, t)*(diff(u(x, t), x)), t, s) = x*(s^2+2)/s^3

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s*laplace(u(x, t), t, s)+laplace(u(x, t)*(diff(u(x, t), x)), t, s) = x*(s^2+2)/s^3

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lap := s^alpha*laplace(u(x, t), t, s) = x*(s^2+2)/s^3-laplace(u(x, t)*(diff(u(x, t), x)), t, s)

s^alpha*laplace(u(x, t), t, s) = x*(s^2+2)/s^3-laplace(u(x, t)*(diff(u(x, t), x)), t, s)

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laplace(u(x, t), t, s) = (x*(s^2+2)/s^3-laplace(u(x, t)*(diff(u(x, t), x)), t, s))/s^alpha

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lap3 := u(x, t) = t^alpha*x/GAMMA(alpha+1)+2*x*t^(alpha+2)/GAMMA(alpha+3)-invlaplace(laplace(u(x, t)*(diff(u(x, t), x)), t, s)/s^alpha, s, t)

u(x, t) = t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha)-invlaplace(laplace(u(x, t)*(diff(u(x, t), x)), t, s)/s^alpha, s, t)

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NULL

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NULL

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u[1](x, t) = -invlaplace(laplace(u[0](x, t)*(diff(u[0](x, t), x)), t, s)/s^alpha, s, t)

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"u[0](x,t):=(t^alpha x)/(GAMMA(1+alpha))+(2 x t^(alpha+2))/(GAMMA(3+alpha))"

proc (x, t) options operator, arrow, function_assign; t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha) end proc

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for j from 0 to 3 do A[j] := subs(lambda = 0, (diff(f(seq(sum(lambda^i*u[i](x, t), i = 0 .. 20), m = 1 .. 2)), [`$`(lambda, j)]))/factorial(j)) end do

(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))

u[1](x, t)*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))+(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(diff(u[1](x, t), x))

u[2](x, t)*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))+u[1](x, t)*(diff(u[1](x, t), x))+(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(diff(u[2](x, t), x))

u[3](x, t)*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))+u[2](x, t)*(diff(u[1](x, t), x))+u[1](x, t)*(diff(u[2](x, t), x))+(t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(diff(u[3](x, t), x))

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S1 := u[1](x, t) = -invlaplace((t^alpha*x/GAMMA(1+alpha)+2*x*t^(alpha+2)/GAMMA(3+alpha))*(t^alpha/GAMMA(1+alpha)+2*t^(alpha+2)/GAMMA(3+alpha))/s^alpha, s, t)

u[1](x, t) = -x*(t^alpha)^2*invlaplace(s^(-alpha), s, t)*(1/GAMMA(1+alpha)^2+4*t^2/(GAMMA(3+alpha)*GAMMA(1+alpha))+4*t^4/GAMMA(3+alpha)^2)

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u[1](x, t) = x*GAMMA(2*alpha+1)*t^(3*alpha)/(GAMMA(1+alpha)^2*GAMMA(3*alpha+1))-4*x*GAMMA(2*alpha+3)*t^(3*alpha+2)/(GAMMA(1+alpha)*GAMMA(3+alpha)*GAMMA(3*alpha+3))-4*`xΓ`(2*alpha+5)/(GAMMA(3+alpha)^2*GAMMA(3*alpha+3))