A novel B-spline method to analyze convection-diffusion-reaction problems in anisotropic inhomogeneous medium

2020 ◽  
Vol 118 ◽  
pp. 216-224
Author(s):  
Sergiy Reutskiy ◽  
Yuhui Zhang ◽  
Ji Lin ◽  
Jun Lu ◽  
Haifeng Xu ◽  
...  
Keyword(s):  
Inhomogeneous Medium ◽  
Diffusion Reaction ◽  
Spline Method ◽  
B Spline ◽  
Convection Diffusion

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.

Are actuarial crop insurance rates fair?: an analysis using a penalized bivariate B ‐spline method

2019 ◽  
Vol 68 (5) ◽  
pp. 1207-1232 ◽  
Author(s):  
Michael J. Price ◽  
Cindy L. Yu ◽  
David A. Hennessy ◽  
Xiaodong Du
Keyword(s):  
Crop Insurance ◽  
Spline Method ◽  
B Spline ◽  
Insurance Rates

scholarly journals Numerical approximation for the solution of linear sixth order boundary value problems by cubic B-spline

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
A. Khalid ◽  
M. N. Naeem ◽  
P. Agarwal ◽  
A. Ghaffar ◽  
Z. Ullah ◽  
...  
Keyword(s):  
Numerical Approximation ◽  
Analytic Solution ◽  
Linear Equations ◽  
Computational Cost ◽  
Spline Method ◽  
System Of Linear Equations ◽  
Approximation Solution ◽  
B Spline ◽  
Novel Technique ◽  
Derivatives Of

AbstractIn the current paper, authors proposed a computational model based on the cubic B-spline method to solve linear 6th order BVPs arising in astrophysics. The prescribed method transforms the boundary problem to a system of linear equations. The algorithm we are going to develop in this paper is not only simply the approximation solution of the 6th order BVPs using cubic B-spline, but it also describes the estimated derivatives of 1st order to 6th order of the analytic solution at the same time. This novel technique has lesser computational cost than numerous other techniques and is second order convergent. To show the efficiency of the proposed method, four numerical examples have been tested. The results are described using error tables and graphs and are compared with the results existing in the literature.

scholarly journals Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 469 ◽  
Author(s):  
Azhar Iqbal ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spline Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
B Spline

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

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