# Quadratic spline collocation for one-dimensional linear parabolic partial differential equations

@article{Christara2009QuadraticSC, title={Quadratic spline collocation for one-dimensional linear parabolic partial differential equations}, author={Christina C. Christara and Tong Chen and Duy Minh Dang}, journal={Numerical Algorithms}, year={2009}, volume={53}, pages={511-553} }

New methods for solving general linear parabolic partial differential equations (PDEs) in one space dimension are developed. The methods combine quadratic-spline collocation for the space discretization and classical finite differences, such as Crank-Nicolson, for the time discretization. The main computational requirements of the most efficient method are the solution of one tridiagonal linear system at each time step, while the resulting errors at the gridpoints and midpoints of the space… CONTINUE READING

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