Solving a nonlinear inverse system of Burgers equations
Authors
Abstract:
By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additionally, obtained numerical results of the cubic B-spline method are compared to trigonometric cubic B-spline method, exponential cubic B-spline method and radial basis function method. Implementation simplicity and less computational cost are the main advantages of proposed scheme compared to previous proposals.
similar resources
Solving a system of 2D Burgers' equations using Semi-Lagrangian finite difference schemes
In this paper, we aim to generalize semi-Lagrangian finite difference schemes for a system of two-dimensional (2D) Burgers' equations. Our scheme is not limited by the Courant-Friedrichs-Lewy (CFL) condition and therefore we can apply larger step size for the time variable. Proposed schemes can be implemented in parallel very well and in fact, it is a local one-dimensional (LOD) scheme which o...
full textSolving a System of Nonlinear Equations
Typical measures of computational efficiency are: 1. the number of function evaluations, 2. the number of iterations required to solve the nonlinear system of equations, and 3. the computational cost per iteration. It is important to keep in mind that the overall cost of solving the system of equations depends on the number of iterations required to achieve some prescribed precision in all the ...
full textSolving System of Nonlinear Equations by using a New Three-Step Method
In this paper, we suggest a fifth order convergence three-step method for solving system of nonlinear equations. Each iteration of the method requires two function evaluations, two first Fr'{e}chet derivative evaluations and two matrix inversions. Hence, the efficiency index is $5^{1/({2n+4n^{2}+frac{4}{3}n^{3}})}$, which is better than that of other three-step methods. The advant...
full textNon-polynomial Spline Method for Solving Coupled Burgers Equations
In this paper, non-polynomial spline method for solving Coupled Burgers Equations are presented. We take a new spline function. The stability analysis using Von-Neumann technique shows the scheme is unconditionally stable. To test accuracy the error norms 2L, L are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equation...
full textglobal results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Relativistic Burgers and Nonlinear Schrödinger Equations
Relativistic complex Burgers-Schrödinger and Nonliner Schrödinger equations are constructed. In the non-relativistic limit they reduce to the standard Burgers and NLS equations respectively and are integrable at any order of relativistic corrections. 1 General Burgers-Schrödinger Hierarchy The relativistic linear Schrödinger equation has been discussed at the early years of quantum mechanics bu...
full textMy Resources
Journal title
volume 10 issue 1
pages 35- 54
publication date 2019-11-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023