@Preben Alsholm 

Thank you very much for your help. It helps a lot in helping me to understand the whole algorithm of solving this PDE.

@Preben Alsholm 

Thank you very much for your help. It helps a lot in helping me to understand the whole algorithm of solving this PDE.

@Preben Alsholm 

Hi,

First of all, thank you very much for helping me out with solving this equation. I have a question to ask regarding the Maple code that you have written.

restart;
pde := diff(u(x, t), t)+diff(u(x, t), x)+u(x, t)=Dirac(x-1);
pde2:=PDEtools:-dchange({x=tau+y,t=tau-y,u(x,t)=w(y,tau)},pde,[y,tau,w]);

For pde, the equation is in the form du/dt + du/dx + u = Dirac(x-1), whereas for the second pde, the equation is in the form of dw/dtau + u(w,tau) = Dirac(x-1). Why is one of the terms missing on the left hand side in pde2?

I'd appreciate it very much if you can help me to clear my doubt.

Thank you once again for your time and help.

@Preben Alsholm 

Hi,

First of all, thank you very much for helping me out with solving this equation. I have a question to ask regarding the Maple code that you have written.

restart;
pde := diff(u(x, t), t)+diff(u(x, t), x)+u(x, t)=Dirac(x-1);
pde2:=PDEtools:-dchange({x=tau+y,t=tau-y,u(x,t)=w(y,tau)},pde,[y,tau,w]);

For pde, the equation is in the form du/dt + du/dx + u = Dirac(x-1), whereas for the second pde, the equation is in the form of dw/dtau + u(w,tau) = Dirac(x-1). Why is one of the terms missing on the left hand side in pde2?

I'd appreciate it very much if you can help me to clear my doubt.

Thank you once again for your time and help.

@Preben Alsholm 

Hi, first of all, many thanks for your suggestion. I am trying to understand how the solution, u(x,t) is obtained manually for the following PDE:

The solution, u(x,t) for this equation is

Where should I start from to get this answer?

Thanks.

@Preben Alsholm 

Hi, first of all, many thanks for your suggestion. I am trying to understand how the solution, u(x,t) is obtained manually for the following PDE:

The solution, u(x,t) for this equation is

Where should I start from to get this answer?

Thanks.

@Preben Alsholm 

Hi there, sorry to bother you again. I've tried to solve this same PDE using a numerical method (ForwardTime1Space_backward) using the following commands:

> pde := diff(u(x, t), t)+diff(u(x, t), x)+0.591e-1*u(x, t)=447213595.5*Dirac(x-200)+1043498389.5*Dirac(x-500);
> IBC := {u(x,0) = 100000000,u(0,t) = 100000000};
> pds := pdsolve(pde,IBC,numeric,time = t, range = 0..100,method = ForwardTime1Space[backward]);
> p1 := pds:-plot(t = 0, numpoints = 50):p2 := pds:-plot(t = 1/8, numpoints = 50, color = blue):p3 := pds:-plot(t = 1/4, numpoints = 50, color = green):plots[display]({p1, p2, p3});

At the range of 0..100, I've managed to obtained a graphical output. However, when I changed the range to 0..1000, I faced an error where it says "unable to compute solution for t<HFloat(0.0):solution becomes undefined etc.)

Do you know any workaround this issue?

Thanks.

@Preben Alsholm 

Hi there, sorry to bother you again. I've tried to solve this same PDE using a numerical method (ForwardTime1Space_backward) using the following commands:

> pde := diff(u(x, t), t)+diff(u(x, t), x)+0.591e-1*u(x, t)=447213595.5*Dirac(x-200)+1043498389.5*Dirac(x-500);
> IBC := {u(x,0) = 100000000,u(0,t) = 100000000};
> pds := pdsolve(pde,IBC,numeric,time = t, range = 0..100,method = ForwardTime1Space[backward]);
> p1 := pds:-plot(t = 0, numpoints = 50):p2 := pds:-plot(t = 1/8, numpoints = 50, color = blue):p3 := pds:-plot(t = 1/4, numpoints = 50, color = green):plots[display]({p1, p2, p3});

At the range of 0..100, I've managed to obtained a graphical output. However, when I changed the range to 0..1000, I faced an error where it says "unable to compute solution for t<HFloat(0.0):solution becomes undefined etc.)

Do you know any workaround this issue?

Thanks.

@Preben Alsholm 

Hi there,

Got the solution as wanted. Thanks a lot for your patience and guidance!

@Preben Alsholm 

Hi there,

Got the solution as wanted. Thanks a lot for your patience and guidance!

Hi,

First of all, many thanks to you for helping me out with solving the PDE. After obtaining u(x,t), I wanted to plot the result for t=0 till t=100 seconds. Using the command

plot(res,t=0..100);

I faced an error regarding invalid input. Do you know any workaround this issue?

Thank you for your time and help.

Hi,

First of all, many thanks to you for helping me out with solving the PDE. After obtaining u(x,t), I wanted to plot the result for t=0 till t=100 seconds. Using the command

plot(res,t=0..100);

I faced an error regarding invalid input. Do you know any workaround this issue?

Thank you for your time and help.