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Orthogonal spline collocation scheme for multiterm fractional convection‐diffusion equation with variable coefficients
Author(s) -
Yang Xuehua,
Zhang Haixiang,
Xu Da
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22213
Subject(s) - orthogonal collocation , mathematics , variable (mathematics) , convection–diffusion equation , collocation method , collocation (remote sensing) , spline (mechanical) , mathematical analysis , partial differential equation , diffusion , space (punctuation) , ordinary differential equation , differential equation , computer science , physics , machine learning , thermodynamics , operating system
The orthogonal spline collocation (OSC) technique is an efficient way to solve a wide variety of problems that are modeled by ordinary and partial differential equations. In this article, by using OSC method in spatial direction and classical L1 approximation in temporal direction, a fully discrete scheme is established for a class of two‐dimensional multiterm fractional convection‐diffusion reaction equation with variable coefficients. The optimal estimates in H j ( j = 0, 1, 2) norms at each time step are derived. Also,L ∞estimate in space is provided. At last, we provide some numerical results to verify the accuracy and efficiency of the proposed algorithm.