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...

As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${cal O}(h^{8})$ convergence analysis, mainly base...

In this paper, we used the Optimal Homotopy Asymptotic Method (OHAM) to find the approximate solution of seventh order linear and nonlinear boundary value problems. The approximate solution using OHAM is compared with Variational Iteration Method (VIM) and exact solutions, an excellent agreement has been observed. The approximate solution of the equations is obtained in terms of convergent seri...

The optimization of an optical system benefits greatly from a study of its aberrations and an identification of each of its elements’ contribution to the overall aberration figures. The matrix formalism developed by one of the authors was the object of a previous paper and allows the expression of image-space coordinates as high-order polynomials of object-space coordinates. In this paper we ap...

The leapfrog time-stepping scheme makes no amplitude errors when integrating linear oscillations. Unfortunately, the Robert-Asselin filter, which is used to damp the computational mode, introduces first-order amplitude errors. The Robert-Asselin-Williams (RAW) filter, which was recently proposed as an improvement, eliminates the first-order amplitude errors and yields third-order amplitude accu...