We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using seventh degree B-Spline function. Formulation is based on particular terms order problem. obtain Septic formulation and Collocation B-spline Method formulated as an approximation solution. apply presented to solve example seventh-order which results show that there...

An overlapping domain decomposition, additive Schwarz, conjugate gradient method is presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicu-bics is applied to the Dirichlet problem for Poisson's equation on a rectangle .

In this paper, we develop a collocation method based on cubic B-spline to the solution of nonlinear parabolic equation εuxx = a(x, t)ut + φ(x, t, u, ux) subject to appropriate initial, and Dirichlet boundary conditions, where ε > 0 is a small constant. We developed a new two-level three-point scheme of order O(k + h). The convergence analysis of the method is proved. Numerical results are given...

This note is inspired by the paper of Bialecki, Fairweather, and Bennett [1] which studies a method for the numerical solution of u00 = f on an interval, and u = f on a rectangle, with zero boundary data; their scheme calculates that C piecewise cubic U for which U 00 (or U) agrees with f at the two (or four) Gauss quadrature points of each subdivision of the original domain. They observe that ...

The quintic B-spline collocation method is developed to solve the fourth-order parabolic partial differential equation. This kind of problem arises in the field of transverse vibration of the uniform flexible beam. Stability analysis of the method has also been proven. Two examples have been considered to illustrate the efficiency of the method developed. It has been observed that the numerical...