A three-point time discretization technique for parabolic partial differential equations

2011 ◽  
Vol 35 (3) ◽  
pp. 406-418 ◽  
Author(s):  
A. Khoshghalb ◽  
N. Khalili ◽  
A. P. S. Selvadurai
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Discretization ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Discretization Technique

scholarly journals A Numerical Method of High Accuracy for Linear Parabolic Partial Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Jun Liu ◽  
Yan Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Computational Cost ◽  
Time Discretization ◽  
Parabolic Partial Differential Equations ◽  
Spline Collocation ◽  
Partial Differential ◽  
Quadratic Spline ◽  
Space Partition ◽  
Gauss Method

We report a new numerical algorithm for solving one-dimensional linear parabolic partial differential equations (PDEs). The algorithm employs optimal quadratic spline collocation (QSC) for the space discretization and two-stage Gauss method for the time discretization. The new algorithm results in errors of fourth order at the gridpoints of both the space partition and the time partition, and large time steps are allowed to save computational cost. The stability of the new algorithm is analyzed for a model problem. Numerical experiments are carried out to confirm the theoretical order of accuracy and demonstrate the effectiveness of the new algorithm.

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