Polynomial particular solutions for certain partial differential operators

Keywords

Mathematics, Partial differential equation, Boundary value problem, Collocation method, Spectral method

References

• The method of fundamental solutions for elliptic boundary value problemsGraeme Fairweather, Andréas Karageorghis — 1998
• Boundary integral methods : numerical and mathematical aspectsMichael A. Golberg — 1999
• Discrete projection methods for integral equationsMichael A. Golberg, C. S. Chen — 1996
• Some Aspects of the Method of Fundamental Solutions for Certain Harmonic ProblemsYiorgos‐Sokratis Smyrlis, Andréas Karageorghis — 2002
• On the dual reciprocity boundary element methodYinglong Zhang — 1993
• The Numerical Evaluation of Particular Solutions for Poisson's EquationKendall Atkinson — 1985
• Fundamental Solutions Method for Elliptic Boundary Value ProblemsAlexander Bogomolny — 1985
• Approximation results for orthogonal polynomials in Sobolev spacesClaudio Canuto, Alfio Quarteroni — 1982
• A new approach to free vibration analysis using boundary elementsDario Nardini, C. A. Brebbia — 1983
• The method of fundamental solutions for linear diffusion-reaction equationsKarthik Balakrishnan, P.A. Ramachandran — 2000
• Improved multiquadric approximation for partial differential equationsMichael A. Golberg, C.S. Chen, Sriganesh R. Karur — 1996
• Particular solutions of Helmholtz-type operators using higher order polyhrmonic splinesAngel Muleshkov, Michael A. Golberg, C. S. Chen — 1999
• Rothe's Method for the Heat Equation and Boundary Integral EquationsRoman Chapko, Rainer Kreß — 1997
• The method of fundamental solutions for inhomogeneous elliptic problemsAndreas Poullikkas, Andréas Karageorghis, Georgios C. Georgiou — 1998
• Dual-reciprocity BEM based on global interpolation functionsAlexander H.‐D. Cheng, Olu Lafe, S. T. Grilli — 1994
• The Numerical Evaluation Of ParticularSolutions For Poisson's Equation - A RevisitC.S. Chen, Angel Muleshkov, Michael A. Golberg — 1999
• Spectral methods for fluid dynamicsM. Yousuff Hussaini, T. A. Zang — 1987
• Spectral Methods In Fluid DynamicsM. Yousuff Hussaini — 1987
• Spectral Methods in Fluid DynamicsClaudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni — 1988
• Handbook of Numerical AnalysisE. Christiansen — 1996

Cited by

• Boundary Control for Inverse Cauchy Problems of the Laplace EquationsLeevan Ling, Tomoya Takeuchi — 2008
• A Novel Semi-Analytic Meshless Method for Solving TwoandThree-Dimensional Elliptic Equations of GeneralForm with Variable Coefficients in Irregular DomainsSergiy Reutskiy — 2014
• Trefftz Methods for Time Dependent Partial Differential EquationsHokwon A. Cho, Michael A. Golberg, Angel Muleshkov — 2004
• Trefftz solution for boundary value problem of three-dimensional Poisson equationEisuke Kita, Yoichi Ikeda, Norio Kamiya — 2005
• The Laplace transform and polynomial Trefftz method for a class of time dependent PDEsWeibin Kong, Xionghua Wu — 2009
• Automatic particular solutions of arbitrary high-order splines associated with polyharmonic and poly-Helmholtz equationsChia‐Cheng Tsai — 2011
• A meshless method for nonhomogeneous polyharmonic problems using method of fundamental solution coupled with quasi-interpolation techniqueXiaolin Li, Shuling Li — 2011
• The method of particular solutions for solving axisymmetric polyharmonic and poly-Helmholtz equationsChia‐Cheng Tsai, C.S. Chen, Tai‐Wen Hsu — 2009
• A method for solving partial differential equations via radial basis functions: Application to the heat equationMehdi Tatari, Mehdi Dehghan — 2010
• Exponential convergence and H‐c multiquadric collocation method for partial differential equationsAlexander H.‐D. Cheng, Michael A. Golberg, E.J. Kansa — 2003
• Particular solutions of splines and monomials for polyharmonic and products of Helmholtz operatorsChia‐Cheng Tsai, Alexander H.‐D. Cheng, C.S. Chen — 2009
• Particular solutions of the multi-Helmholtz-type equationAngel Muleshkov, Michael A. Golberg — 2007
• Method of particular solutions for nonlinear Poisson-type equations in irregular domainsSergiy Reutskiy — 2013
• A new scheme for the solution of reaction diffusion and wave propagation problemsJi Lin, Wen Chen, C.S. Chen — 2014
• The method of approximate fundamental solutions (MAFS) for elliptic equations of general type with variable coefficientsSergiy Reutskiy — 2012
• Differential quadrature Trefftz method for Poisson-type problems on irregular domainsXionghua Wu, Huijing Du, Weibin Kong — 2008
• The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadingsChia‐Cheng Tsai — 2010
• Multiquadric and Chebyshev approximation to three-dimensional thermoelasticity with arbitrary body forcesChia‐Cheng Tsai, Tai‐Wen Hsu — 2013
• Method of particular solutions for solving PDEs of the second and fourth orders with variable coefficientsSergiy Reutskiy — 2013
• The method of fundamental solutions for solving incompressible Navier–Stokes problemsD.L. Young, Yi-Ting Lin, Chia‐Ming Fan — 2009

Related papers

• An efficient spectral collocation algorithm for nonlinear Phi-four equationsAli H Bhrawy, Laila M Assas, Mohammed Alghamdi — 2013
• Applications of Legendre spectral collocation method for solving system of time delay differential equationsSami Ullah Khan, Ishtiaq Ali — 2020
• A collocation spectral method for two-dimensional Sobolev equationsShiju Jin, Zhendong Luo — 2018
• A spectral collocation method for mixed functional differential equationsReuben Rauch, Manfred R. Trummer, Jim Williams — 2020
• Spectral Collocation Method for Parabolic Partial Differential Equations with Neumann Boundary ConditionsMohammad Javidi, A. Golbabai — 2007
• Jacobi Collocation Methods for Solving Generalized Space-Fractional Burgers’ EquationsQingqing Wu, Xiaoyan Zeng — 2019
• Chebyshev Spectral Collocation Method for Computing Numerical Solution of Telegraph EquationMohammad Javidi — 2013
• Numerical solution of stochastic partial differential equations using a collocation methodMinoo Kamrani — 2016
• Legendre–Gauss collocation methods for ordinary differential equationsBen‐yu Guo, Zhongqing Wang — 2009
• Comparison of Numerical Approximations of One-Dimensional Space Fractional Diffusion Equation Using Different Types of Collocation Points in Spectral Method Based on Lagrange’s Basis PolynomialsMushfika Hossain Nova, Hasib Uddin Molla, Sajeda Banu — 2017