Pass Additional Arguments into Guess Function for BVP

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Paul Safier
Paul Safier 2025-5-9
编辑： Torsten 2025-5-9
In the example given here:
Matlab BVP Example
What would be the syntax (if it's even possible) to pass an additional argument(s) into the guess function?
This is how it is currently written:
function yinit = mat4init(x) % initial guess function
yinit = [cos(4*x)
-4*sin(4*x)];
end
It fails if I do this:
solinit = bvpinit(linspace(0,pi,10),@mat4init,lambda,param);
function yinit = mat4init(x,param) % initial guess function
yinit = [cos(param*x)
-4*sin(param*x)];
end
I want to pass arrays/parameters into the guess function because the call to the function to solve my BVP will occur within another code and the proper initial guess will evolve/change for each call.
Thanks!

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采纳的回答

Torsten
Torsten 2025-5-9
编辑：Torsten 2025-5-9
Ran in:
lambda = 15;
additional_parameters = 22;
solinit = bvpinit(linspace(0,pi,10),@(x)mat4init(x,additional_parameters),lambda);
additional_parameters = 22
additional_parameters = 22
additional_parameters = 22
additional_parameters = 22
additional_parameters = 22
additional_parameters = 22
additional_parameters = 22
additional_parameters = 22
additional_parameters = 22
additional_parameters = 22
sol = bvp4c(@mat4ode, @mat4bc, solinit);
fprintf('Fourth eigenvalue is approximately %7.3f.\n',...
sol.parameters)
Fourth eigenvalue is approximately 17.097.
xint = linspace(0,pi);
Sxint = deval(sol,xint);
plot(xint,Sxint)
axis([0 pi -4 4])
title('Eigenfunction of Mathieu''s Equation.')
xlabel('x')
ylabel('y')
legend('y','y''')
●
function dydx = mat4ode(x,y,lambda) % equation being solved
q = 5;
dydx = [y(2)
-(lambda - 2*q*cos(2*x))*y(1)];
end
function res = mat4bc(ya,yb,lambda) % boundary conditions
res = [ya(2)
yb(2)
ya(1)-1];
end
function yinit = mat4init(x,additional_parameters) % initial guess function
additional_parameters
yinit = [cos(4*x)
-4*sin(4*x)];
end
  4 个评论
显示 2更早的评论
Paul Safier
Paul Safier 2025-5-9
This is it:
t2 = interp1(xx(2:end),diff(tstArray)/(dx),x,"linear","extrap");
Thanks for the help, @Torsten
Torsten
Torsten 2025-5-9
编辑：Torsten 2025-5-9
Ran in:
The problem is that you cannot interpolate the derivative at x if x is in the interval from xx(1) to xx(2) with the command
t2 = interp1(xx(2:end),diff(tstArray)/(dx),x);
Better compute an approximation to the derivative function using "gradient" instead of "diff" and before calling bvp4c:
lambda = 15;
xx = linspace(0,pi,20);
tstArray = cos(4*xx);
der_tstArray = gradient(tstArray,xx(2)-xx(1));
solinit = bvpinit(linspace(0,pi,10),@(x)mat4init(x,xx,tstArray,der_tstArray),lambda);
sol = bvp4c(@mat4ode, @mat4bc, solinit);
fprintf('Fourth eigenvalue is approximately %7.3f.\n',...
sol.parameters)
Fourth eigenvalue is approximately 17.097.
xint = linspace(0,pi);
Sxint = deval(sol,xint);
plot(xint,Sxint)
axis([0 pi -4 4])
title('Eigenfunction of Mathieu''s Equation.')
xlabel('x')
ylabel('y')
legend('y','y''')
function dydx = mat4ode(x,y,lambda) % equation being solved
q = 5;
dydx = [y(2)
-(lambda - 2*q*cos(2*x))*y(1)];
end
function res = mat4bc(ya,yb,lambda) % boundary conditions
res = [ya(2)
yb(2)
ya(1)-1];
end
function yinit = mat4init(x,xx,tstArray,der_tstArray) % initial guess function
t1 = interp1(xx,tstArray,x);
t2 = interp1(xx,der_tstArray,x);
yinit = [t1
t2];
%yinit = [cos(4*x)
% -4*sin(4*x)];
end

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