2026-09-21T18:21:08Zhttps://bura.brunel.ac.uk/oai/request

oai:bura.brunel.ac.uk:2438/75922014-11-01T11:27:17Zcom_2438_23com_2438_58com_2438_8627com_2438_8620col_2438_3672col_2438_8629col_2438_235

Mikhailov, SE Mohamed, Nurul Akmal 2013-07-12T13:32:45Z 2013-07-12T13:32:45Z 2013 http://bura.brunel.ac.uk/handle/2438/7592 This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University. A numerical implementation of the direct Boundary-Domain Integral Equation (BDIE)/ Boundary-Domain Integro-Differential Equations (BDIDEs) and Localized Boundary-Domain Integral Equation (LBDIE)/Localized Boundary-Domain Integro-Differential Equations (LBDIDEs) related to the Neumann and Dirichlet boundary value problem for a scalar elliptic PDE with variable coefficient is discussed in this thesis. The BDIE and LBDIE related to Neumann problem are reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretisation of the BDIE/BDIDEs and LBDIE/LBDIDEs with quadrilateral domain elements leads to systems of linear algebraic equations (discretised BDIE/BDIDEs/LBDIE/BDIDEs). Then the systems obtained from BDIE/BDIDE (discretised BDIE/BDIDE) are solved by the LU decomposition method and Neumann iterations. Convergence of the iterative method is analyzed in relation with the eigen-values of the corresponding discrete BDIE/BDIDE operators obtained numerically. The systems obtained from LBDIE/LBDIDE (discretised LBDIE/LBDIDE) are solved by the LU decomposition method as the Neumann iteration method diverges. Submitted by Lesh Gowreesunker (lesh.gowreesunker@brunel.ac.uk) on 2013-07-12T13:32:34Z No. of bitstreams: 1 FulltextThesis.pdf: 881179 bytes, checksum: 53a799f575fa4e4356a6e941ca3801df (MD5) Approved for entry into archive by Lesh Gowreesunker(lesh.gowreesunker@brunel.ac.uk) on 2013-07-12T13:32:45Z (GMT) No. of bitstreams: 1 FulltextThesis.pdf: 881179 bytes, checksum: 53a799f575fa4e4356a6e941ca3801df (MD5) Made available in DSpace on 2013-07-12T13:32:45Z (GMT). No. of bitstreams: 1 FulltextThesis.pdf: 881179 bytes, checksum: 53a799f575fa4e4356a6e941ca3801df (MD5) This study was funded by the Malaysian Ministry of Higher Education and Sultan Idris Education University. en Brunel University, School of Information Systems, Computing and Mathematics School of Information Systems, Computing and Mathematics http://bura.brunel.ac.uk/bitstream/2438/7592/1/FulltextThesis.pdf Localised boundary-domain integral equation Spectrum Neumann series Bilinear interpolation Semi-analytic method Numerical solution and spectrum of boundary-domain integral equations Thesis