The Rothe-Newton approach to simulate the variable coefficient convection-diffusion equations

Document Type : Research Paper


1 Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

2 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China

3 Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan

4 Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy

5 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran


The current article presents a novel hybrid approach based on the Rothe time-marching algorithm and a spectral matrix collocation approach using the well-known Newton bases to deal with the spatial variable. Utilizing the Rothe approach converts the underlying convection-diffusion into initial-boundary value problems and then the Newton collocation method solves the continuous discretized time equation in each time step. The error analysis of the newly employed basis functions is established. Three numerical simulations are developed to show the accuracy and utility of the proposed hybrid strategy.
Applying the current study to other linear and nonlinear PDEs and high-order PDEs can be performed straightforwardly.


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