Method of fundamental solutions for a conductivity problem
Applied Mathematics in Science and EngineeringA numerical solution of the interior Dirichlet problem for the homogeneous conductivity equation is considered. After introducing certain assumptions and discretization of the domain, the boundary value problem for a second-order elliptic equation with ...
Andriy Beshley, Ihor Borachok
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The method of fundamental solutions for Helmholtz-type problems [PDF]
, 2013 The purpose of this thesis is to extend the range of application of the method fundamental solutions (MFS) to solve direct and inverse geometric problems associated with two- or three-dimensional Helmholtz-type equations.
Bin-Mohsin, Bandar Abdullah
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Observations on the basic (G′/G)-expansion method for finding solutions to nonlinear evolution equations [PDF]
, 2010 The extended tanh-function expansion method for finding solutions to nonlinear evolution equations delivers solutions in a straightforward manner and in a neat and helpful form.
Parkes, E.J.
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Applicability and applications of the method of fundamental solutions [PDF]
Mathematics of Computation, 2009 In the present work, we investigate the applicability of the method of fundamental solutions for the solution of boundary value problems of elliptic partial differential equations and elliptic systems. More specifically, we study whether linear combinations of fundamental solutions can approximate the solutions of the boundary ...
Smyrlis, Yiorgos-Sokratis +1 more
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Solitary-wave solutions of the Degasperis-Procesi equation by means of the homotopy analysis method [PDF]
, 2010 The homotopy analysis method is applied to the Degasperis-Procesi equation in order to find analytic approximations to the known exact solitary-wave solutions for the solitary peakon wave and the family of solitary smooth-hump waves.
Abbasbandy, S., Parkes, E.J.
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A well conditioned Method of Fundamental Solutions
CoRR, 2021 The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and boundary conditions.
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The method of fundamental solutions for pointwise source reconstruction
Computers & Mathematics with Applications, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rocha de Faria, J +3 more
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A method of fundamental solutions without fictitious boundary [PDF]
Engineering Analysis with Boundary Elements, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Wen, Wang, F. Z.
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Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations [PDF]
, 2010 The 'tanh-coth expansion method' for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature. It is a natural extension to the basic tanh-function expansion method which was developed in the
Parkes, E.J.
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A modified version of regularized meshless method for three dimensional potential problem
ITM Web of Conferences, 2017 In this study, three-dimensional potential problem is solved using a novel meshless method. Due to the singularity of the kernel functions, the diagonal terms of the influence matrices in the method of fundamental solutions (MFS) are unobtainable.
Lai Cheng-Yang +3 more
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