javid basha jv

## 8 Badges

6 years, 340 days

## How to obtain a solution using pdsolve...

Maple 18

Dear maple users

Greetings.

In this code, I am solving the PDEs via perturbation method.

There is some mistake in the boundary condition and pdsolve.

Kindly help me that to get the solution for this PDE via perturbation method.

Wating for your replay.

BC:

Code: JVB.mw

## dsolve not working for N=1 or N=2....

Maple 18

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));

## How to avoid the white patches in figure...

Maple 18

Dear maple users,

Greetings.

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

How to avoid such patches.

## How to obtain a solution for bvp...

Maple 18

Dear maple users,

Greetings.

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Download JVB.mw

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

waiting for your reply.

## Outcomes are not matching...

Maple 18

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.

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