You may find this answer helpful https://www.mathworks.com/matlabcentral/answers/170648-how-can-i-solve-systems-of-pdes-with-three-independent-variables-by-using-the-pdepe-solver-of-the-ma

Solving partial differential equations (PDEs) with three independent variables in MATLAB can be a complex task depending on the specific form of the PDE. MATLAB provides several functions for solving PDEs, and the choice of method depends on the nature of your problem.

Here's a general outline of the steps you might take:

Here's a simple example using pdepe for a one-dimensional problem:

matlabCopy codefunction pdex1 m = 0; x = linspace(0,1,100); t = linspace(0,1,10); sol = pdepe(m, @pdex1pde, @pdex1ic, @pdex1bc, x, t); u = sol(:,:,1); surf(x,t,u) title('Numerical solution computed with 20 mesh points'); xlabel('Distance x'); ylabel('Time t'); zlabel('u(x,t)'); end function [c,f,s] = pdex1pde(x,t,u,DuDx) c = 1; f = DuDx; s = 0; end function u0 = pdex1ic(x) u0 = sin(pi*x); end function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t) pl = ul; ql = 0; pr = ur - 1; qr = 0; end