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.

ABSORBING BOUNDARY CONDITIONS IN BLOCK GAUSS–SEIDEL METHODS FOR CONVECTION PROBLEMS

1996 ◽  
Vol 06 (04) ◽  
pp. 481-502 ◽  
Author(s):  
FREDERIC NATAF
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Convection Diffusion ◽  
Radiation Boundary Conditions ◽  
Convection Diffusion Equation ◽  
Numerical Tests ◽  
Radiation Boundary ◽  
Theoretical Results

In the context of convection-diffusion equation, the use of absorbing boundary conditions (also called radiation boundary conditions) is considered in block Gauss–Seidel algorithms. Theoretical results and numerical tests show that the convergence is thus accelerated.

Approximation of 3D convection diffusion equation using DQM based on modified cubic trigonometric B-splines

2020 ◽  
pp. 1-10
Author(s):  
Mohammad Tamsir ◽  
Neeraj Dhiman ◽  
F.S. Gill ◽  
Robin
Keyword(s):  
Diffusion Equation ◽  
Numerical Solutions ◽  
Basis Functions ◽  
B Spline ◽  
Convection Diffusion ◽  
B Splines ◽  
Convection Diffusion Equation ◽  
First Order ◽  
The Stability ◽  
Derivatives Of

This paper presents an approximate solution of 3D convection diffusion equation (CDE) using DQM based on modified cubic trigonometric B-spline (CTB) basis functions. The DQM based on CTB basis functions are used to integrate the derivatives of space variables which transformed the CDE into the system of first order ODEs. The resultant system of ODEs is solved using SSPRK (5,4) method. The solutions are approximated numerically and also presented graphically. The accuracy and efficiency of the method is validated by comparing the solutions with existing numerical solutions. The stability analysis of the method is also carried out.

scholarly journals B-Spline Solution for a Convection-Diffusion Equation

2014 ◽  
Vol 125 (2) ◽  
pp. 548-550 ◽  
Author(s):  
H. Caglar ◽  
N. Caglar ◽  
M. Ozer
Keyword(s):  
Diffusion Equation ◽  
B Spline ◽  
Convection Diffusion ◽  
Convection Diffusion Equation
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