Abstract
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 of order of seventh order boundary value problem. We obtain Septic B-Spline formulation and the Collocation B-spline Method is formulated as an approximation solution. We apply the presented method to solve an example of seventh-order boundary value problem which the results show that there is an agreement between approximate solutions and exact solutions. Resulting low absolute errors show that the presented numerical method is effective for solving high order boundary value problems. Finally, a general conclusion has been included.
Highlights
IntroductionNew Cubic B-Spline Approximation for Solving Linear Two-Point Boundary-Value Problems is presented by Busyra Latif, and Samsul Ariffin Abdul Karim [8]
We apply the presented method to solve an example of seventh order boundary value problem in which the result shows that there is an agreement between approximate solutions and exact solutions
Maximum absolute error and approximate solution yi coming from the presented method and exact solution Yi for this problem are shown in Table 4, which the analytical solution is (1− x) ex
Summary
New Cubic B-Spline Approximation for Solving Linear Two-Point Boundary-Value Problems is presented by Busyra Latif, and Samsul Ariffin Abdul Karim [8]. This method is based on cubic B-spline basis functions with a new approximation for the second order derivative. For finding the numerical solution of a particular case of seventh order linear boundary value problems where some terms of the boundary value problem are zero, we use B-Spline Basis and collocation method which is considered as approximation solution, considering a generic case with a general form of Boundary value problem including term of B-spline basis functions with higher derivatives in the general form of the boundary value problem results in a dense linear system that takes more computational costs with each added term. The term “spline” is used to refer to a wide class of functions that are used in applications requiring data interpolation or smoothing
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