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Title: Localized direct boundary–domain integro–differential formulations for scalar nonlinear boundary-value problems with variable coefficients
Authors: Mikhailov, SE
Keywords: Compressible flow;Heat transfer;Integro-differential equations;Mesh-based and mesh-less algorithms;Partial differential equations
Issue Date: 2005
Publisher: Springer
Citation: Journal of Engineering Mathematics 51(3): 283-302, Mar 2005
Abstract: Mixed boundary-value Problems (BVPs) for a second-order quasi-linear elliptic partial differential equation with variable coefficients dependent on the unknown solution and its gradient are considered. Localized parametrices of auxiliary linear partial differential equations along with different combinations of the Green identities for the original and auxiliary equations are used to reduce the BVPs to direct or two-operator direct quasi-linear localized boundary-domain integro-differential equations (LBDIDEs). Different parametrix localizations are discussed, and the corresponding nonlinear LBDIDEs are presented. Mesh-based and mesh-less algorithms for the LBDIDE discretization are described that reduce the LBDIDEs to sparse systems of quasi-linear algebraic equations.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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