Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter

Das, P. C.; Vigo‐Aguiar, Jesús

doi:10.1016/j.cam.2017.11.026

Cited by 82 publications

(30 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We show that the present approach can lead to the exact solution of the problem and hence can be considered as an alternative way of the methods given in the references. ()…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…We show that the present approach can lead to the exact solution of the problem and hence can be considered as an alternative way of the methods given in the references. 14,15 Example 1. Let us consider the following nonlinear fractional Volterra-Fredholm integro-differential equation for approximate solution:…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Here, we are interested in obtaining the solution of fractional nonlinear integro-differential equations by using semi-analytical homotopy-based perturbation methods. [6][7][8] This approach makes the approximation simple for complicated models and can be considered as an alternative way to avoid the numerical discretizations provided in other works [9][10][11][12][13][14][15] for perturbation problems. Furthermore, the present method is not only an effective tool for approximation of the solution but it can also provide the exact solution of certain problems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Homotopy perturbation method for solving Caputo‐type fractional‐order Volterra‐Fredholm integro‐differential equations

Das

Rana

Ramos

2019

Comp and Math Methods

Self Cite

View full text Add to dashboard Cite

This work considers the solution of fractional Volterra‐Fredholm integro‐differential equations. Here, we consider the approximation of the solution based on semi‐analytical approaches. We use the homotopy perturbation method approach for this purpose. It is observed through different examples that the adopted strategy is not only an effective tool for approximation of the solution but also can lead to the exact solution of certain problems.

show abstract

“…We show that the present approach can lead to the exact solution of the problem and hence can be considered as an alternative way of the methods given in the references. ()…”

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Homotopy perturbation method for solving Caputo‐type fractional‐order Volterra‐Fredholm integro‐differential equations

Das

Rana

Ramos

2019

Comp and Math Methods

Self Cite

View full text Add to dashboard Cite

show abstract

“…To obtain such a mesh, we use the idea of equidistribution principle which has been applied to a wide range of practical problems (see, e.g. [6,9,16,19,20]). A mesh Ω K is said to be equidistributed, if…”

Section: Adaptive Time Meshes Via Equidistributionmentioning

confidence: 99%

An adaptive moving mesh method for a time-fractional Black–Scholes equation

2019

View full text Add to dashboard Cite

In this paper we study the numerical method for a time-fractional Black-Scholes equation, which is used for option pricing. The solution of the fractional-order differential equation may be singular near certain domain boundaries, which leads to numerical difficulty. In order to capture the singular phenomena, a numerical method based on an adaptive moving mesh is developed. A finite difference method is used to discretize the time-fractional Black-Scholes equation and error analysis for the discretization scheme is derived. Then, an adaptive moving mesh based on an a priori error analysis is established by equidistributing monitor function. Numerical experiments support these theoretical results. MSC: 65M06; 65M12; 65M15

show abstract

“…Note: Algorithms have been produced lately to solve ODEs and PDEs by moving grids, the latest papers which show its effectiveness can be read in [19], [20], [21], [22], [23], [24], [32] and [33]. These references provide the technique that show the moving mesh algorithm and the discrete problem can be patched up to find the solution on adaptive mesh.…”

Section: Numerical Grid Generationmentioning

confidence: 99%

Optimal Control Approach to Image Registration

Salako¹

2018

ujam

View full text Add to dashboard Cite

We discuss the orthogonality problem of moving grids, where we minimize a cost function with a regularization term and improve the orthogonality of grids by making the angle between grids close to 90  .The initial grid used is obtained by a well-established method known as the grid deformation method. We will then replace the cost function in the orthogonality problem with sum of squared differences (SSD) to discuss the image registration problem. We will discuss the non-uniqueness of solutions, existence of optimal solutions and prove the existence of Lagrange multipliers of the image registration problem using the Direct Method in Calculus of Variation and then derive an optimality system based on the construction of a Lagrangian functional from which optimal transformations can be calculated.

show abstract

Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter

Cited by 82 publications

References 12 publications

Homotopy perturbation method for solving Caputo‐type fractional‐order Volterra‐Fredholm integro‐differential equations

Homotopy perturbation method for solving Caputo‐type fractional‐order Volterra‐Fredholm integro‐differential equations

An adaptive moving mesh method for a time-fractional Black–Scholes equation

Optimal Control Approach to Image Registration

Contact Info

Product

Resources

About