
The Generalized Fractional BenjaminBonaMahony Equation: Analytical and Numerical Results
The generalized fractional BenjaminBonaMahony (gfBBM) equation models ...
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On Theoretical and Numerical Aspect of Fractional Differential Equations with Purely Integral Conditions
In this paper, we are interested in the study of a problem with fraction...
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Convergence of a finite difference scheme for the Kuramoto–Sivashinsky equation defined on an expanding circle
This paper presents a finite difference method combined with the Crank–N...
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Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium
A Dirichlet problem is considered for the eikonal equation in an anisotr...
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A second order difference scheme for time fractional diffusion equation with generalized memory kernel
In the current work we build a difference analog of the Caputo fractiona...
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Temporally semidiscrete approximation of a Dirichlet boundary control for a fractional/normal evolution equation with a final observation
Optimal Dirichlet boundary control for a fractional/normal evolution wit...
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Convergence of the Deep BSDE method for FBSDEs with nonLipschitz coefficients
This paper is dedicated to solve highdimensional coupled FBSDEs with no...
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Second order scheme for selfsimilar solutions of a timefractional porous medium equation on the halfline
Nonlocality in time is an important property of systems in which their present state depends on the history of the whole evolution. Combined with the nonlinearity of the process it poses serious difficulties in both analytical and numerical treatment. We investigate a timefractional porous medium equation that has proved to be important in many applications, notably in hydrology and material sciences. We show that the solution of both free boundary Dirichlet, Neumann, and Robin problems on the halfline satisfies a Volterra integral equation with nonLipschitz nonlinearity. Based on this result we prove existence, uniqueness, and construct a family of numerical methods that solve these equations outperforming the usual naïve finite difference approach. Moreover, we prove the convergence of these methods and illustrate the theory with several numerical examples.
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