High order numerical algorithms based on biquadratic spline collocation for two-dimensional parabolic partial differential equations
作者： Jun Liu , Hui Guo , Yao-Lin Jiang , Yan Wang
DOI: 10.1080/00207160.2018.1437260
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摘要: We report a new algorithm for solving linear parabolic partial differential equations in two space dimension. The employs optimal biquadratic spline collocation discretization a...
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Jim Douglas, Todd Dupont, Collocation Methods for Parabolic Equations in a Single Space Variable ,(1974)
Adem Kaya, Ali Sendur, Finite difference approximations of multidimensional convection-diffusion-reaction problems with small diffusion on a special grid Journal of Computational Physics. ,vol. 300, pp. 574- 591 ,(2015) , 10.1016/J.JCP.2015.08.007
Alok Dutt, Leslie Greengard, Vladimir Rokhlin, Spectral Deferred Correction Methods for Ordinary Differential Equations Bit Numerical Mathematics. ,vol. 40, pp. 241- 266 ,(1998) , 10.1023/A:1022338906936
Chafik Allouch, Paul Sablonnière, Driss Sbibih, A collocation method for the numerical solution of a two dimensional integral equation using a quadratic spline quasi-interpolant Numerical Algorithms. ,vol. 62, pp. 445- 468 ,(2013) , 10.1007/S11075-012-9598-2
Anita T. Layton, On the choice of correctors for semi-implicit Picard deferred correction methods Applied Numerical Mathematics. ,vol. 58, pp. 845- 858 ,(2008) , 10.1016/J.APNUM.2007.03.003
Anita T. Layton, Michael L. Minion, IMPLICATIONS OF THE CHOICE OF QUADRATURE NODES FOR PICARD INTEGRAL DEFERRED CORRECTIONS METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Bit Numerical Mathematics. ,vol. 45, pp. 341- 373 ,(2005) , 10.1007/S10543-005-0016-1
Bernard Bialecki, Ryan I. Fernandes, An Alternating Direction Implicit Backward Differentiation Orthogonal Spline Collocation Method for Linear Variable Coefficient Parabolic Equations SIAM Journal on Numerical Analysis. ,vol. 47, pp. 3429- 3450 ,(2009) , 10.1137/080739112
B. Bialecki, G. Fairweather, A. Karageorghis, Q.N. Nguyen, Optimal superconvergent one step quadratic spline collocation methods Bit Numerical Mathematics. ,vol. 48, pp. 449- 472 ,(2008) , 10.1007/S10543-008-0188-6
Adem Kaya, Finite difference approximations of multidimensional unsteady convection-diffusion-reaction equations Journal of Computational Physics. ,vol. 285, pp. 331- 349 ,(2015) , 10.1016/J.JCP.2015.01.024
Christina C. Christara, Quadratic spline collocation methods for elliptic partial differential equations BIT. ,vol. 34, pp. 33- 61 ,(1994) , 10.1007/BF01935015