clear all; close all;
% Grid:
N = 2^8; L = 10;
x2 = linspace(-L/2,L/2,N+1);
x = x2(1:N);
dx = x(2) - x(1);
% Diffusion parameter:
kappa = .5;
% Time span for solution:
tspan = [0:1:10];
% Create sparse D2 matrix:
e1 = ones(N,1);
A = spdiags([e1 -2*e1 e1],[-1 0 1],N,N);
A(1,N) = 1;
A(N,1) = 1;
% Create initial condition:
U0 = exp(-x.^2);
% Call ODE solver:
[t,U] = ode45('heat_1d_rhs',tspan,U0,[],kappa,dx,A);