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Quadratic spline collocation for one-dimensional linear parabolic partial differential equations. (English) Zbl 1189.65235
The authors focus on numerical methods for general linear differential equations of parabolic type posed on one space dimension. The numerical methods rely on quadratic-spline collocation combined with the classical finite difference method. The main results of the paper provide stability and convergence properties of the discretized solution. The final part of the article contains various numerical experiments that sustain the theoretical findings. The new methods developed by the authors are also applied to American put option pricing problem in the paper with satisfactory results.

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
91G60 Numerical methods (including Monte Carlo methods)
Full Text: DOI
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