CIR-scheme-initial1.m

%CIR scheme - function 1
clc;
clear;
close all;
format long
%define variables
xmin = 0;
xmax = 1;
N = 50;
dt = 0.009;
t = 0;
tmax = 0.1;
C = 1;

%discretise the domain
dx = (xmax - xmin)/N;
x = xmin - dx : dx : xmax + dx;

%initial condition
u0 = sin (2*pi*x);
u1 = u0;
u2 = u0;
u3 = u0;
u4 = u0;
un1 = u0;
un2 = u0;
un3 = u0;
un4 = u0;

lambda1 = 0.25;
lambda2 = 0.5;
lambda3 = 0.75;
lambda4 = 1.0;
%time loop
nsteps = tmax/dt;
for n =1 : nsteps
    %boundary cond
    u1(1)=sin(2*pi*(t-0.5));
    u2(1)=sin(2*pi*(t-0.5));
    u3(1)=sin(2*pi*(t-0.5));
    u4(1)=sin(2*pi*(t-0.5));
    %calculate CIR scheme
    for i = 2:N+2
        un1(i) = u1(i) - lambda1*(u1(i)-u1(i-1));
    end
    for i = 2:N+2
        un2(i) = u2(i) - lambda2*(u2(i)-u2(i-1));
    end
    for i = 2:N+2
        un3(i) = u3(i) - lambda3*(u3(i)-u3(i-1));
    end
    for i = 2:N+2
        un4(i) = u4(i) - lambda4*(u4(i)-u4(i-1));
    end
    %exact
    exact = sin (2*pi*(x - C*t));
    %update
    t = t+dt;
    u1 = un1;
    u2 = un2;
    u3 = un3;
    u4 = un4;
    %plot
    plot(x,exact,'r-');
    hold on
    plot (x,u1,'--','markerfacecolor','g');
    plot (x,u2,'--','markerfacecolor','b');
    plot (x,u3,'--','markerfacecolor','k');
    plot (x,u4,'--','markerfacecolor','r');
    hold off
    legend('exact sol','lambda = 0.25','lambda = 0.50','lambda = 0.75','lambda = 1.00');
    axis([xmin,xmax,-1.5,1.5])
    xlabel('x','fontsize',16)
    ylabel('U(t,x)','fontsize',16)
    title(sprintf('time = %1.2f',t),'fontsize',16)
    shg
    pause(dt);
end