Solving Boundary Value problems via Orthogonal Collocation

We continue with boundary value problems this time using a method often referred to as orthogonal collocation. In previous videos, we approximated a differential equation with a system of coupled algebraic equations. This system was often fairly large, say 100 or more coupled equations. This method allows (in some cases) to represent the differential equation by a handful of algebraic equations (though the matrices involved are not sparse). This potentially allows us to solve complicated systems much faster.

Github: https://github.com/kpmooney/numerical_methods_youtube/blob/master/bvp/Orthogonal%20Collocation.ipynb

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