Orthogonal collocation

Orthogonal collocation is a method for the numerical solution of partial differential equations. It uses collocation at the zeros of some orthogonal polynomials to transform the partial differential equation (PDE) to a set of ordinary differential equations (ODEs). The ODEs can then be solved by any method. It has been shown that it is usually advantageous to choose the collocation points as the zeros of the corresponding Jacobi polynomial (independent of the PDE system). Orthogonal collocation is a method for the numerical solution of partial differential equations. It uses collocation at the zeros of some orthogonal polynomials to transform the partial differential equation (PDE) to a set of ordinary differential equations (ODEs). The ODEs can then be solved by any method. It has been shown that it is usually advantageous to choose the collocation points as the zeros of the corresponding Jacobi polynomial (independent of the PDE system).