Numerical techniques for a parabolic equation subject to an overspecified boundary condition

Dehghan, Mehdi

doi:10.1016/s0096-3003(01)00194-1

Cited by 11 publications

(3 citation statements)

References 19 publications

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“…Table 1: A comparison between absolute error obtained by the methods of [3][4] and the presented method when T = 0.5 , h = 1 50 , k = 0.0001 for w(x, T ). x…”

Section: Multigrid Algorithmmentioning

confidence: 99%

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A computational source modeling of brain activity: An inverse problem

Rasanan

Rad

2022

J Neurodev Cogn

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Source determination in an inverse problem from the over-specified data plays a crucial role in cognitive modeling. In this paper, an accurate and fast method is proposed for solving the one-dimensional inverse problem concerning diffusion equation with source control parameter. The proposed method is based on applying a compact finite difference scheme for spatial components and solving the system that arised from this scheme by multigrid.

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“…Table 1: A comparison between absolute error obtained by the methods of [3][4] and the presented method when T = 0.5 , h = 1 50 , k = 0.0001 for w(x, T ). x…”

Section: Multigrid Algorithmmentioning

confidence: 99%

“…A comparison between absolute error obtained by the methods of[3][4] and the presented method when T = 0.5 , h = 1 50 , k = 0.0001 for p(t). tExact p Method of[3] Method of[4] Presented method by v-cycle v 1 = v 2 = 4…”

mentioning

confidence: 99%

A computational source modeling of brain activity: An inverse problem

Rasanan

Rad

2022

J Neurodev Cogn

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“…In recent years, much attention has been given to solving the multi‐point boundary value problems 1–3. Several numerical and analytical techniques are being developed for solving these problems 1, 4–8. In this paper, we shall give a numerical method that is different from Reference 1 dependent on reproducing kernel theory.…”

Section: Introductionmentioning

confidence: 99%

A numerical solution to nonlinear multi-point boundary value problems in the reproducing kernel space

Yang

Cui

2010

Math. Meth. Appl. Sci.

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In this paper, a new numerical algorithm is provided to solve nonlinear multi-point boundary value problems in a very favorable reproducing kernel space, which satisfies all complex boundary conditions. Its reproducing kernel function is discussed in detail. The theorem proves that the approximate solution and its first-and second-order derivatives all converge uniformly. The numerical experiments show that the algorithm is quite accurate and efficient for solving nonlinear multi-point boundary value problems.

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The radial basis functions method for identifying an unknown parameter in a parabolic equation with overspecified data

Dehghan

Tatari

2007

Numerical Methods Partial

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Parabolic partial differential equations with overspecified data play a crucial role in applied mathematics and engineering, as they appear in various engineering models. In this work, the radial basis functions method is used for finding an unknown parameter p(t) in the inverse linear parabolic partial differential equationwhere u is unknown while the initial condition and boundary conditions are given. Also an additional condition for known functions E(t), k(x), is given as the integral overspecification over the spatial domain. The main approach is using the radial basis functions method. In this technique the exact solution is found without any mesh generation on the domain of the problem. We also discuss on the case that the overspecified condition is in the formu(x, t)dx = E(t), 0 < t ≤ T , 0 < s(t) < 1, where s and E are known functions. Some illustrative examples are presented to show efficiency of the proposed method.

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Numerical techniques for a parabolic equation subject to an overspecified boundary condition

Cited by 11 publications

References 19 publications

A computational source modeling of brain activity: An inverse problem

A computational source modeling of brain activity: An inverse problem

A numerical solution to nonlinear multi-point boundary value problems in the reproducing kernel space

The radial basis functions method for identifying an unknown parameter in a parabolic equation with overspecified data

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