A WEIGHTED LEAST SQUARES B-SPLINE COLLOCATION METHOD FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

Infimum D. Yulamda, Mas Irfan P. Hidayat

Abstract


A new, free-integration approach based upon B-spline for solving boundary value problem is introduced and presented in the paper, called weighted least squares B-spline collocation method. It combines high order B-spline basis functions with high approximation and continuity properties and weighted least squares method which is robust to deal with scattered or randomly knot points distribution. In addition, using appropriate designed B-spline basis function construction, the new approach introduces no difficulties in imposing both Dirichlet and Neumann boundary conditions in the problem domain. As a result, the effectiveness of the new approach is greatly enhanced with the flexibility to cope with both regular and irregular shaped domains. Numerical examples show the applicability and capability of the new approach for solving elliptic partial differential equations in arbitrary domains.

Keywords


Weighted B-splines; least square; approximation; meshless; arbitrary domains; elliptic PDEs

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DOI: http://dx.doi.org/10.12962/j2746279X.v1i2.16946

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