A Method of Solution for the One-Dimensional Heat Equation Subject to Nonlocal Conditions

Ang, W.T.

doi:10.1007/s100120200039

Cited by 39 publications

(34 citation statements)

References 6 publications

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“…Along a different line, problems for parabolic equations that combine classical and integral conditions were considered by Ang [51], Batten [52], Cannon [12,13] [79], and Yurchuk [81].…”

Section: Introductionmentioning

confidence: 99%

On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation

Dehghan

2004

Numerical Methods Partial

200

123

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Numerical solution of hyperbolic partial differential equation with an integral condition continues to be a major research area with widespread applications in modern physics and technology. Many physical phenomena are modeled by nonclassical hyperbolic boundary value problems with nonlocal boundary conditions. In place of the classical specification of boundary data, we impose a nonlocal boundary condition. Partial differential equations with nonlocal boundary specifications have received much attention in last 20 years. However, most of the articles were directed to the second-order parabolic equation, particularly to heat conduction equation. We will deal here with new type of nonlocal boundary value problem that is the solution of hyperbolic partial differential equations with nonlocal boundary specifications. These nonlocal conditions arise mainly when the data on the boundary can not be measured directly. Several finite difference methods have been proposed for the numerical solution of this one-dimensional nonclassic boundary value problem. These computational techniques are compared using the largest error terms in the resulting modified equivalent partial differential equation. Numerical results supporting theoretical expectations are given. Restrictions on using higher order computational techniques for the studied problem are discussed. Suitable references on various physical applications and the theoretical aspects of solutions are introduced at the end of this article.

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“…Along a different line, problems for parabolic equations that combine classical and integral conditions were considered by Ang [51], Batten [52], Cannon [12,13] [79], and Yurchuk [81].…”

Section: Introductionmentioning

confidence: 99%

On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation

Dehghan

2004

Numerical Methods Partial

200

123

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“…Along a different line, problems for parabolic equations that combine classical and integral conditions were considered by Ang [11], Cannon et al [12][13][14][15], Dehghan [16][17][18], Ekolin [19], Saadatmandi and Razzaghi [20], and Lin and Tiat [21,22].…”

Section: Introductionmentioning

confidence: 98%

Numerical solution of the one‐dimensional wave equation with an integral condition

Saadatmandi

Dehghan

2006

Numerical Methods Partial

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The hyperbolic partial differential equation with an integral condition arises in many physical phenomena. In this research a numerical technique is developed for the one-dimensional hyperbolic equation that combine classical and integral boundary conditions. The proposed method is based on shifted Legendre tau technique. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

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“…Problem (1.1)-( 1.3) is studied by the Rothe method [15]. Ang [2] has considered a one-dimensional heat equation with nonlocal (integral) conditions. The author has taken the laplace transform of the problem and then used numerical technique for the inverse laplace transform to obtain the numerical solution.…”

Section: Introductionmentioning

confidence: 99%

A computational method for integro-differential hyperbolic equation with integral conditions

BOUZIANI¹

2013

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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C o m m u n .Fa c .S c i.U n iv .A n k .S e rie s A 1 Vo lu m e 6 2 , N u m b e r 1 , P a g e s 1 3 1 -1 4 2 (2 0 1 3 ) IS S N 1 3 0 3 -5 9 9 1 A COMPUTATIONAL METHOD FOR INTEGRO-DIFFERENTIAL HYPERBOLIC EQUATION WITH INTEGRAL CONDITIONS* AHCENE MERAD AND ABDELFATAH BOUZIANIAbstract. The subject of this work is to prove existence, uniqueness, and continuous dependence upon the data of solution to integrodi¤erential hyperbolic equation with integral conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, the solution by using a numerical technique for inverting the Laplace transforms is obtained.

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A Method of Solution for the One-Dimensional Heat Equation Subject to Nonlocal Conditions

Cited by 39 publications

References 6 publications

On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation

On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation

Numerical solution of the one‐dimensional wave equation with an integral condition

A computational method for integro-differential hyperbolic equation with integral conditions

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