javid basha jv

## 65 Reputation

3 years, 252 days

## How to solve this PDE equation...

Maple 18

Dear maple users

Greetings.

I hope you are all fine.

In this code, I am solving the PDEs via pdsolve with numeric.

There is some mistake in the boundary condition and pdsolve.

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

In this problem h(z) is piecewise

Bc:

code:JVB.mw

Note: z=0.5:

## How to plot the excel data...

Maple 18

Dear maple users,

Greeting for the day.

I have some data in an excel file. How to plot the excel data in contours with labels.

Also, how to show the x-axis range =-1.5..1.5 and y-axis range = -0.5..1 with the contour sequence -2..2.

XLdat.xlsx

Please see the figure for the model plot.

## 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.

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.

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.

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