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Numerical Solution of Dirichlet Boundary Domain Integro Differential Equation with Less Number of Collocation Points

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dc.contributor.authorNurul Akmal Mohameden_US
dc.contributor.authorNurul Farihan Mohameden_US
dc.contributor.authorNurul Huda Mohameden_US
dc.contributor.authorMohd Rozni Md Yusofen_US
dc.date.accessioned2024-05-28T05:45:12Z
dc.date.available2024-05-28T05:45:12Z
dc.date.issued2016
dc.descriptionVolume: 10 No: 50en_US
dc.description.abstractIn this paper, we show that we have two approaches in implementing of Boundary-Domain Integro-Differential Equation (BDIDE) associated to Dirichlet Boundary Value Problem (BVP) for an elliptic Partial Differential Equation (PDE) with a variable coefficient. One way is by choosing the collocation points at all nodes i.e. on the boundary and interior domain. The other approach is choosing the collocation points for the interior nodes only. We present the numerical implementation of the BDIDE associated to Dirichlet BVP for an elliptic PDE with a variable coefficient by using the second approach. The BDIDE is consisting of several integrals that exhibit singularities. Generally, the integrals are evaluated by using Gauss- Legendre quadrature formula. Our numerical results show that the use of semi-analytic method gives high accuracy results. The discretized BDIDE yields a system of equations. We then apply by a direct method i.e. LU decomposition method to solve the systems of equations. In all the test domains, we present the relative errors of the solutions and the relative error for the gradient.en_US
dc.identifier.doi10.12988/ams.2016.6381
dc.identifier.epage2469
dc.identifier.issn1312-885X
dc.identifier.issue50
dc.identifier.spage2459
dc.identifier.urihttp://www.m-hikari.com/ams/ams-2016/ams-49-52-2016/6381.html
dc.identifier.urihttps://oarep.usim.edu.my/handle/123456789/6343
dc.identifier.volume10
dc.language.isoen_USen_US
dc.publisherHikari LTD.en_US
dc.relation.ispartofApplied Mathematical Sciencesen_US
dc.subjectDirect united boundary-domain integro-differential equation, Dirichlet problem, partial differential equation, semi-analytic integration methoden_US
dc.titleNumerical Solution of Dirichlet Boundary Domain Integro Differential Equation with Less Number of Collocation Pointsen_US
dc.typeArticleen_US
dspace.entity.typePublication

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