Algorithme de la Méthode d'Adams-Bashforth-Moulton pour résoudre les équations différentielles vectorielles en Matlab

Algorithme de la Méthode d'Adams-Bashforth-Moulton pour résoudre les équations différentielles vectorielles en Matlab :

function [t,y] = ode_ABM(f,tspan,y0,N,KC,varargin) %Adams-Bashforth-Moulton method to solve vector d.e. y’(t) = f(t,y(t)) % for tspan = [t0,tf] and with the initial value y0 and N time steps % using the modifier based on the error estimate depending on KC = 1/0 if nargin < 5, KC = 1; end %with modifier by default if nargin < 4 | N < = 0, N = 100; end %default maximum number of iterations y0 = y0(:)’; %make it a row vector h = (tspan(2) - tspan(1))/N; %step size tspan0 = tspan(1)+[0 3]*h; [t,y] = rk4(f,tspan0,y0,3,varargin{:}); %initialize by Runge-Kutta t = [t(1:3)’ t(4):h:tspan(2)]’; for k = 1:4, F(k,:) = feval(f,t(k),y(k,:),varargin{:}); end p = y(4,:); c = y(4,:); KC22 = KC*251/270; KC12 = KC*19/270; h24 = h/24; h241 = h24*[1 -5 19 9]; h249 = h24*[-9 37 -59 55]; for k = 4:N p1 = y(k,:) +h249*F; %Eq.(6.4.8a) m1 = pk1 + KC22*(c-p); %Eq.(6.4.8b) c1 = y(k,:)+ ... h241*[F(2:4,:); feval(f,t(k + 1),m1,varargin{:})]; %Eq.(6.4.8c) y(k + 1,:) = c1 - KC12*(c1 - p1); %Eq.(6.4.8d) p = p1; c = c1; %update the predicted/corrected values F = [F(2:4,:); feval(f,t(k + 1),y(k + 1,:),varargin{:})]; End