HIGH ORDER B-SPLINE COLLOCATION METHOD AND ITS APPLICATION FOR HEAT TRANSFER PROBLEMS

High order B-spline collocation for solving boundary value problem is presented in this paper. The approach employs high order B-spline basis functions with high approximation and continuity properties to handle problem domain with scattered or random distribution of knot points.  Using appropriate B-spline basis function construction, the new approach introduces no difficulties in imposing both Dirichlet and Neumann boundary conditions in the problem domain. Several numerical examples in arbitrary domains, both regular and irregular shaped domains, are considered in the present study. In addition, simulation results concerning with heat transfer applications are further presented and discussed

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

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