High Accuracy Iterative Solution of Convection Diffusion Equation with Boundary Layers on Nonuniform Grids

2001 ◽  
Vol 171 (2) ◽  
pp. 560-578 ◽  
Author(s):  
Lixin Ge ◽  
Jun Zhang
Keyword(s):  
Diffusion Equation ◽  
Boundary Layers ◽  
Iterative Solution ◽  
High Accuracy ◽  
Nonuniform Grids ◽  
Convection Diffusion ◽  
Convection Diffusion Equation

scholarly journals Novel Cubic Trigonometric B-Spline Approach Based on the Hermite Formula for Solving the Convection-Diffusion Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Aatika Yousaf ◽  
Thabet Abdeljawad ◽  
Muhammad Yaseen ◽  
Muhammad Abbas
Keyword(s):  
Approximate Solution ◽  
Diffusion Equation ◽  
Time Derivative ◽  
High Accuracy ◽  
Spline Method ◽  
B Spline ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Numerical Tests ◽  
Piecewise Continuous

This paper introduces a cubic trigonometric B-spline method (CuTBM) based on the Hermite formula for numerically handling the convection-diffusion equation (CDE). The method utilizes a merger of the CuTBM and the Hermite formula for the approximation of a space derivative, while the time derivative is discretized using a finite difference scheme. This combination has greatly enhanced the accuracy of the scheme. A stability analysis of the scheme is also presented to confirm that the errors do not magnify. The main advantage of the scheme is that the approximate solution is obtained as a smooth piecewise continuous function empowering us to approximate a solution at any location in the domain of interest with high accuracy. Numerical tests are performed, and the outcomes are compared with the ones presented previously to show the superiority of the presented scheme.

Sign in / Sign up

Export Citation Format

Share Document