On solvability of the integrodifferential hyperbolic equation with purely nonlocal conditions

Merad, Ahcene; Bouziani, Abdelfatah; Özel, Cenap; Kılıçman, Adem

doi:10.1016/s0252-9602(15)30006-0

Cited by 8 publications

(8 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some recent results on the existence and uniqueness of solution for such problems can be found [4][5][6][7]. For instance, we can mention the following works: Dabas and Bahuguna [4] have investigated the nonlocal initial-boundary value problem for linear parabolic integro-differential equation, the authors have applied Rothe's method to establish the existence and uniqueness result for (6)- (9).…”

Section: H(t − S)u(x S)ds = G(x T) (X T) ∈mentioning

confidence: 99%

“…In [7] authors have proved the existence, uniqueness and continuous dependence on the data of solution for (15)- (17).…”

Section: H(t − S)u(x S)ds = G(x T) (X T) ∈mentioning

confidence: 99%

“…The problem (15)–(17) is studied by the Galerkin method in , the authors have established the existence and uniqueness of a generalized solution. In authors have proved the existence, uniqueness and continuous dependence on the data of solution for (15)–(17).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solving nonlocal initial‐boundary value problems for parabolic and hyperbolic integro‐differential equations in reproducing kernel hilbert space

Fardi

Ghasemi

2016

Numerical Methods Partial

View full text Add to dashboard Cite

This article is concerned with a method for solving nonlocal initial-boundary value problems for parabolic and hyperbolic integro-differential equations in reproducing kernel Hilbert space. Convergence of the proposed method is studied under some hypotheses which provide the theoretical basis of the proposed method and some error estimates for the numerical approximation in reproducing kernel Hilbert space are presented. Finally, two numerical examples are considered to illustrate the computation efficiency and accuracy of the proposed method.

show abstract

Section: H(t − S)u(x S)ds = G(x T) (X T) ∈mentioning

confidence: 99%

“…In [7] authors have proved the existence, uniqueness and continuous dependence on the data of solution for (15)- (17).…”

Section: H(t − S)u(x S)ds = G(x T) (X T) ∈mentioning

confidence: 99%

See 1 more Smart Citation

Solving nonlocal initial‐boundary value problems for parabolic and hyperbolic integro‐differential equations in reproducing kernel hilbert space

Fardi

Ghasemi

2016

Numerical Methods Partial

View full text Add to dashboard Cite

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: 99%

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

“…Considerable work has been made on the area of nonlocal boundary values problems in the numerical and theoretical aspects. Indeed theoretical studies devoted to these classes of problems are usually connected with some difficulties due to the presence of an integral terms in the boundary conditions, this promoted researchers to perform some modifications and improvements on the classical methods to overcome this issue (see, e.g., [2,3,12,16]).…”

Section: Introductionmentioning

confidence: 99%

Numerical solution for a class of parabolic integro-differential equations subject to integral boundary conditions

Chattouh

2022

Arab. J. Math.

View full text Add to dashboard Cite

Many physical phenomena can be modelled through nonlocal boundary value problems whose boundary conditions involve integral terms. In this work we propose a numerical algorithm, by combining second-order Crank–Nicolson schema for the temporal discretization and Legendre–Chebyshev pseudo-spectral method (LC–PSM) for the space discretization, to solve a class of parabolic integrodifferential equations subject to nonlocal boundary conditions. The approach proposed in this paper is based on Galerkin formulation and Legendre polynomials. Results on stability and convergence are established. Numerical tests are presented to support theoretical results and to demonstrate the accuracy and effectiveness of the proposed method

show abstract

On solvability of the integrodifferential hyperbolic equation with purely nonlocal conditions

Cited by 8 publications

References 19 publications

Solving nonlocal initial‐boundary value problems for parabolic and hyperbolic integro‐differential equations in reproducing kernel hilbert space

Solving nonlocal initial‐boundary value problems for parabolic and hyperbolic integro‐differential equations in reproducing kernel hilbert space

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

Numerical solution for a class of parabolic integro-differential equations subject to integral boundary conditions

Contact Info

Product

Resources

About