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Mathematics
Differential Equations
Inverse ODE, Green's Functions, and series solution
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[QUOTE="member 428835, post: 6000312"] This is what I thought, but are you sure? Attached is a plot where I have basis functions ##\phi_i = x^i##. In one case I've recombined each ##x^i## beforehand and defined ##\phi_i## to be these recombined polynomials such that they automatically satisfy the boundary conditions. Another case I simply use ##\phi_i##. Notice recombining satisfies boundaries, but not recombining does not. Additionally, both techniques give the correct eigenvalues. It seems recombining is necessary; can you explain why not recombining won't work? [/QUOTE]
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Differential Equations
Inverse ODE, Green's Functions, and series solution
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