Vectorized Relaxation Algorithm For Solving Linear Partial Differential Equations

This program utilizes a vectorized relaxation algorithm in order to solve linear partial differential equations. Please submit any suggestions you have for improving the program (I would eventually like to include a convergence constant in order to implement the SOR method).Example:%This is an example of how to use the program for a parallel plate capacitor with random point charges in the grid space:%sets a plot constant to plot data train every 100 loop counts plotk=100;%Here are the grid dimensions (note that the grid need not be square) L_xspan=150; L_yspan=150;meshdim=1; %set the unit height of the grid points tol=10^(-7); %tolerance%places the plates in the center of the grid with an x length 5 plate1=L_xspan/2-5; plate2=L_yspan/2+5;%separates the plates by 10 grid units position_plate1=L_yspan/2-5:L_yspan/2+5; position_plate2=L_yspan/2-5:L_yspan/2+5;%creates the walls of the grid and capacitor plates Bound_0_x={1:L_xspan;1:L_xspan;1;L_xspan;plate1;plate2}; Bound_0_y={1;L_yspan;1:L_yspan;1:L_yspan;position_plate1;position_plate2};%sets the voltage of either plate v1=175; v2=-175;%sets the values of the grid walls at zero and inserts the capacitor plate voltages Bound_0_val=[0;0;0;0;v1;v2];%generates 5 random gridpoints Random_gridpoints=round(100*rand(2,5));%generates 5 random potentials Random_potentials=round(100*rand(1,5));%inserts initial values for the random potentials that were generated init_x={Random_gridpoints(1,1);Random_gridpoints(1,2);Random_gridpoints(1,3);Random_gridpoints(1,4);Random_gridpoints(1,5)}; init_y={Random_gridpoints(2,1);Random_gridpoints(2,2);Random_gridpoints(2,3);Random_gridpoints(2,4);Random_gridpoints(2,5)}; init_val=[Random_potentials(1,1);-Random_potentials(1,2);Random_potentials(1,3);Random_potentials(1,4);-Random_potentials(1,5)];%calls the function [array_f,X,Y] = FDRelax(meshdim,L_xspan,L_yspan,Bound_0_x,... Bound_0_y,Bound_0_val,init_x,init_y,... init_val,tol,plotk);