Inversion Laplace transform for Integrodifferential Parabolic Equation with Purely Nonlocal conditions

Merad, Ahcene

doi:10.15672/hjms.2015449667

Cited by 4 publications

(5 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Laplace transform is an efficient method for solving many differential equations and partial differential equations. The main difficulty with Laplace transform method, is inverting the domain of Laplace solution into the real domain (see [4,[20][21][22]). In this section we shall apply the Laplace transform technique to find solutions of partial differential equations.…”

Section: Laplace Transform Methods and Stehfest Algorithmmentioning

confidence: 99%

Laplace Transform and Homotopy Perturbation Methods for Solving the Pseudohyperbolic Integrodifferential Problems with Purely Integral Conditions

Necib¹,

Merad²

2020

KgJMat

Self Cite

View full text Add to dashboard Cite

In this paper we defined and investigated the various properties of a class of pseudohyperbolic equation defined on purely integral (nonlocal) conditions. We proved the uniqueness and the existence of the solution using energy inequality (A priori estimates). We found a semi analytical solution using the Laplace transform and Stehfest algorithm method. Next, we used another method called the Homotopy perturbation. Finally, we give some examples for illustration.

show abstract

Section: Laplace Transform Methods and Stehfest Algorithmmentioning

confidence: 99%

Laplace Transform and Homotopy Perturbation Methods for Solving the Pseudohyperbolic Integrodifferential Problems with Purely Integral Conditions

Necib¹,

Merad²

2020

KgJMat

Self Cite

View full text Add to dashboard Cite

show abstract

“…Similar problem can be found in [14]. Recently, various types of partial differential equations (PDEs) with nonlocal conditions have been studied in [2-4, 10, 11, 18, 19] among others, and the use of nonlocal conditions was extended to cover a wide variety of PDEs, and integro-differential equations; see, e.g., [13,15,16,22]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 96%

“…For other models, we refer the reader to [6,18,21]. The problem (1.1)-(1.3) is studied by using the Rothe method in [13], the existence and uniqueness of solution to this problem is given in [15], where the proofs are based on a priori estimates and Laplace transform method. On the other hand, in [1], the author considered a one-dimensional heat equation with nonlocal integral conditions and applied the Laplace transform to the problem.…”

Section: Introductionmentioning

confidence: 99%

Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials

Bencheikh¹,

Chiter²,

Li³

2018

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

Some problems from modern physics and science can be described in terms of partial differential equations with nonlocal conditions. In this paper, a numerical method which employs the orthonormal Bernstein polynomials basis is implemented to give the approximate solution of integro-differential parabolic equation with purely nonlocal integral conditions. The properties of orthonormal Bernstein polynomials, and the operational matrices for integration, differentiation and the product are introduced and are utilized to reduce the solution of the given integro-differential parabolic equation to the solution of algebraic equations. An illustrative example is given to demonstrate the validity and applicability of the new technique.

show abstract

“…Nowadays various nonlocal problems for partial differential equations have been actively studied and one can find a lot of papers dealing with them (see [13]- [29] , [12]- [21] and references therein). Afterwards, the nonlocal problems for integro-differential equation with integral conditions was studied by many authors, see A. Merad and A. Bouziani [23] , [26]. Motivated by this we study a parabolic integrodifferential equation with nonlocal second kind integral condition.…”

Section: Introductionmentioning

confidence: 98%

Study of Solution for a Parabolic Integrodifferential Equation with the Second Kind Integral Condition

2018

ijaa

View full text Add to dashboard Cite

In this paper, we establish sufficient conditions for the existence, uniqueness and numerical solution for a parabolic integrodifferential equation with the second kind integral condition. The existence, uniqueness of a strong solution for the linear problem based on a priori estimate "energy inequality" and transformation of the linear problem to linear first-order ordinary differential equation with second member. Then by using a priori estimate and applying an iterative process based on results obtained for the linear problem, we prove the existence, uniqueness of the weak generalized solution of the integrodifferential problem. Also we have developed an efficient numerical scheme, which uses temporary problems with standard boundary conditions. A suitable combination of the auxiliary solutions defines an approximate solution to the original nonlocal problem, the algebraic matrices obtained after the full discretization are tridiagonal, then the solution is obtained by using the Thomas algorithm. Some numerical results are reported to show the efficiency and accuracy of the scheme.

show abstract

Inversion Laplace transform for Integrodifferential Parabolic Equation with Purely Nonlocal conditions

Cited by 4 publications

References 21 publications

Laplace Transform and Homotopy Perturbation Methods for Solving the Pseudohyperbolic Integrodifferential Problems with Purely Integral Conditions

Laplace Transform and Homotopy Perturbation Methods for Solving the Pseudohyperbolic Integrodifferential Problems with Purely Integral Conditions

Solving parabolic integro-differential equations with purely nonlocal conditions by using the operational matrices of Bernstein polynomials

Study of Solution for a Parabolic Integrodifferential Equation with the Second Kind Integral Condition

Contact Info

Product

Resources

About