non linear partial diferential equation

Hello

I need to insert this equation in MATLAB

would you please help me. I have no Idea

It may similar to heat equation, but there are some extra terms which I do not know how to deal with.

[Xianglin]

May I ask which term you do not know how to deal with?

Answer 1

[Torsten]

I don't see a similarity to the heat equation.

You will have to discretize the left-hand side of the equation and use ode15s to solve for H in the grid points in X-direction.

Look up "method-of-lines" for more details.

"sign" is "sign" in MATLAB and "absolute value" is "abs" in MATLAB.

[sepideh]

Dear Torsten

I searched about MOL, but still its not clear for me how to deal with That H which is multiplied into the sqaure root inside the derivative.

I saw several examples of Burger's equation with the form which had been solved by this method. I understand now what you mean by discretisizing L.H.S ,but I still dont know hnow to encounter H in those formulas.

[Torsten]

I don't know which discretization is optimal in your case, but you could consider approximating

d/dx (H * ( sqrt(1+4*N*abs(dH/dx)) - 1) ) @ X(i) as
{[H * ( sqrt(1+4*N*abs(dH/dx)) - 1)] @ X(i+1/2) - [H * ( sqrt(1+4*N*abs(dH/dx)) - 1)] @X(i-1/2)} / ( X(i+1/2)-X(i-1/2) ) ~
{[(H(i+1)+H(i))/2 * (sqrt(1+4*N*abs((H(i+1)-H(i))/(X(i+1)-X(i))))-1)] - ...
 [(H(i)+H(i-1))/2 * (sqrt(1+4*N*abs((H(i)-H(i-1))/(X(i)-X(i-1))))-1)]} / ( X(i+1/2)-X(i-1/2) ) 

where

X(i+1/2) = (X(i+1)+X(i))/2
X(i-1/2) = (X(i)+X(i-1))/

and assuming that N is a constant.