Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition

Debela, Habtamu Garoma

doi:10.1155/2021/5559486

Cited by 4 publications

(2 citation statements)

References 22 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The existence and uniqueness of the solutions of nonlocal boundary value problems have been studied by many authors [3,23]. Some approaches for the numerical solution of singularly perturbed nonlocal boundary value problems have been proposed in [6,7,11,13,14,15,16,18] and [26]. Uniformly convergent numerical methods of order second and high for solving different singularly perturbed problems have been studied in [5,8,9,10,12,13,14,15,16,27] and [36].…”

Section: Introductionmentioning

confidence: 99%

“…Some approaches for the numerical solution of singularly perturbed nonlocal boundary value problems have been proposed in [6,7,11,13,14,15,16,18] and [26]. Uniformly convergent numerical methods of order second and high for solving different singularly perturbed problems have been studied in [5,8,9,10,12,13,14,15,16,27] and [36]. To the best of our knowledge, the problem under consideration has not been done using nonstandard fitted finite difference method.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust Numerical Method for Singularly Perturbed Convection-Diffusion Type Problems With Non-Local Boundary Condition

Debela

Woldaregay

Duressa

2022

Mathematical Modelling and Analysis

View full text Add to dashboard Cite

This paper presents the study of singularly perturbed differential equations of convection diffusion type with non-local boundary condition. The proposed numerical scheme is a combination of classical finite difference method for the initial boundary condition and nonstandard finite difference method for the differential equations at the interior points. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical examples considered. The method is shown to be first-order convergence independent of the perturbation parameter ε.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Numerical Method for Singularly Perturbed Convection-Diffusion Type Problems With Non-Local Boundary Condition

Debela

Woldaregay

Duressa

2022

Mathematical Modelling and Analysis

View full text Add to dashboard Cite

show abstract

A non-uniform Haar wavelet method for a singularly perturbed convection–diffusion type problem with integral boundary condition on an exponentially graded mesh

Chakravarthy

Sundrani

2023

Comp. Appl. Math.

View full text Add to dashboard Cite

Weighted Average Based Differential Quadrature Method for One-Dimensional Homogeneous First Order Nonlinear Parabolic Partial Differential Equation

Koroche

2021

IJAM

View full text Add to dashboard Cite

In this paper, the weighted average-based differential quadrature method is presented for solving one-dimensional homogeneous first-order non-linear parabolic partial differential equation. First, the given solution domain is discretized by using uniform discretization grid point. Next, by using Taylor series expansion we obtain central finite difference discretization of the partial differential equation involving with temporal variable associated with weighted average of partial derivative concerning spatial variable. From this, we obtain the system of nonlinear ordinary differential equations and it is linearized by using the quasilinearization method. Then by using the polynomial-based differential quadrature method for approximating derivative involving with spatial variable at specified grid point, we obtain the system of linear equation. Then they obtained linear system equation is solved by using the LU matrix decomposition method. To validate the applicability of the proposed method, two model examples are considered and solved at each specific grid point on its solution domain. The stability and convergent analysis of the present method is worked by supported the theoretical and mathematical statements and the accuracy of the solution is obtained. The accuracy of the present method has been shown in the sense of root mean square error norm and maximum absolute error norm and the local behavior of the solution is captured exactly. Numerical versus exact solutions and behavior of maximum absolute error between them have been presented in terms of graphs and the corresponding root mean square error norm and maximum absolute error norm presented in tables. The present method approximates the exact solution very well and it is quite efficient and practically well suited for solving the non-linear parabolic equation. The numerical result presented in tables and graphs indicates that the approximate solution is in good agreement with the exact solution.

show abstract

Exponential Fitted Operator Method for Singularly Perturbed Convection-Diffusion Type Problems with Nonlocal Boundary Condition

Cited by 4 publications

References 22 publications

Robust Numerical Method for Singularly Perturbed Convection-Diffusion Type Problems With Non-Local Boundary Condition

Robust Numerical Method for Singularly Perturbed Convection-Diffusion Type Problems With Non-Local Boundary Condition

A non-uniform Haar wavelet method for a singularly perturbed convection–diffusion type problem with integral boundary condition on an exponentially graded mesh

Weighted Average Based Differential Quadrature Method for One-Dimensional Homogeneous First Order Nonlinear Parabolic Partial Differential Equation

Contact Info

Product

Resources

About