Pass Additional Arguments into Guess Function for BVP

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!

Answer 1

[Torsten]

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

[Paul Safier]

@Torsten Shouldn't this be acceptable though?

lambda = 15;
xx = linspace(0,pi,20);
tstArray = cos(4*xx);

solinit = bvpinit(linspace(0,pi,10),@(x)mat4init(x,xx,tstArray),lambda);

sol = bvp4c(@mat4ode, @mat4bc, solinit);
fprintf('Fourth eigenvalue is approximately %7.3f.\n',...
            sol.parameters)

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) % initial guess function
t1 = interp1(xx,tstArray,x);
dx = xx(2)-xx(1);
t2 = interp1(xx(2:end),diff(tstArray)/(dx),x);
yinit = [t1
        t2];
%yinit = [cos(4*x)
%        -4*sin(4*x)];
end

[Paul Safier]

t2 = interp1(xx(2:end),diff(tstArray)/(dx),x,"linear");

This fails too. This works though:

tstArray2 = -4*sin(4*xx);
solinit = bvpinit(linspace(0,pi,10),@(x)mat4init(x,xx,tstArray,tstArray2),lambda);

function yinit = mat4init(x,xx,tstArray,tstArray2) % initial guess function
t1 = interp1(xx,tstArray,x);
t2 = interp1(xx,tstArray2,x);
yinit = [t1
        t2];
%yinit = [cos(4*x)
%        -4*sin(4*x)];
end

So, maybe something goofy with using diff for the derivative or with extrapolation...?

[Paul Safier]

This is it:

t2 = interp1(xx(2:end),diff(tstArray)/(dx),x,"linear","extrap");

Thanks for the help, @Torsten

[Torsten]

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