Anonymous ODE function syntax for multipoint BVP
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Is there a way to define an anonymous ODE function (in a separate m file) while using bvp4c with multi-point boundary conditions? I tried using the syntax dydx = ODEfun(x,y,k,p) where p is a vector of known parameters and k is the region. The bvp4c syntax I used was: sol = bvp4c(@(x,y,px,k) ODEfun,@(yl,yr) @BCfun, solinit). I get an error saying "Too many input parameters for ODEfun". I can get it to work if the ODEfun is nested as in the threebvp example.
回答（1 个）
Sulaymon Eshkabilov
2021-5-20
In your exercise, a relatively simple solution is to employ the function handles. The suggested approach is shown via Sturm-Liouville BVP example.
% Sturm_Liouville_bvp. Given: -u"+w^2*u=sinh(t)
% periodic boundary conditions: u(0)=u(1)=0
% ----------------------------------------------------------
% Define residues of BCs via a function handle
Res=@(yl,yr)([yl(1) yr(1)]);
% 1st guess solution function defined with function handle:
Gsol1=@(t)([sin(-0.540302305868140*t), cos(t)-0.540302305868140]);
close all; clc
figure
t = linspace(0, 1, 50);
omega = [0, 3, 5, 7, 13];
LABEL = {};
for ii=1:numel(omega)
% A guess structure consisting of time mesh within [0, 1]
% in the range of BCs and a guess function (Gsol):
SOLin1 = bvpinit(linspace(0,1, 10),Gsol1);
% Another numeric value based initial guess y1=0 and y2=0
SOLin2 = bvpinit(linspace(0,1, 10),[0,0]);
% Given problem formulation:
dy=@(t,y)([y(2), omega(ii)^2*y(1)-sinh(t)]);
% Obtain the solutions of the problem for two initial guesses:
SOLs1GUESS = bvp4c(dy,Res,SOLin1);
SOLs2GUESS = bvp4c(dy,Res,SOLin2);
% Compute numeric solutions of the problem within time-space:
y1 = deval(SOLs1GUESS,t);
y2 = deval(SOLs2GUESS,t);
subplot(211)
plot(t, y1(1,1:end), 'o'),
ylabel( 'y(t) solution'), hold all; grid on
LABEL{ii} =(['\leftarrow\omega = ' num2str(omega(ii))]);
legend(LABEL{:})
title(['Simulation of Sturm Liouville BVP: ', '-u"+\omega^2*u=sinh(t), BC: u(0)=u(1)=0'])
subplot(212)
plot(t, y2(1, :), 'p'), grid on
LABEL{ii} =(['\leftarrow\omega = ' num2str(omega(ii))]);
legend(LABEL{:}); hold all
end
gtext('Guess 1: sin and cos fcns', 'background', 'w')
gtext('Guess 2: numerical values', 'background', 'y')
xlabel 't', ylabel( 'y(t) solution')
hold off
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2021-5-20
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