A computational study of the one‐dimensional parabolic equation subject to nonclassical boundary specifications

By Mehdi Dehghan. 2006

166 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/bd041f4ec83a282c4274501b2dab502f7b9d9b4b

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In Applied Mathematics

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition (2008, background): “The presence of integral terms in boundary conditions can greatly complicate the application of standard numerical techniques such as the familiar finite difference schemes, finite element techniques, spectral procedures and boundary element methods [17–19].”
Numerical solution of the one‐dimensional wave equation with an integral condition (2007, methodology): “method introduced in this article is capable of solving the one-dimensional hyperbolic equation with a nonlocal boundary condition and can be considered as an efficient method [29, 30].”
A meshless method using the radial basis functions for numerical solution of the regularized long wave equation (2010, methodology): “It is worth to point out that the new method developed in the current paper can be applied to solve the boundary value problems investigated in [63–66].”
A survey on stationary problems, Green’s functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions (2014, methodology): “A survey of numerical methods for the one-dimensional parabolic equation subject to nonlocal conditions was done by Dehghan [45].”
Use of radial basis functions for solving the second‐order parabolic equation with nonlocal boundary conditions (2008, methodology): “The specification of energy over a certain part of a heat conductor relates physically to the specification of the relative heat content of a portion of the conductor, whereas for diffusion problems this condition is equivalent to the specification of the fluid mass in a portion of the diffusion dom”
Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions (2009, methodology): “It is worth to point out that the RBFs method developed in the current paper can be employed to solve the nonclassic boundary value problems investigated in [38,39].”
High order implicit collocation method for the solution of two‐dimensional linear hyperbolic equation (2009, unknown): “Dehghan [5] used the idea to solve a parabolic partial differential equation with nonclassic initial condition [12,13].”