Cubic splines solutions of the higher order boundary value problems arise in sandwich panel theory

Abstract

An inventive strategy is bestowed here to acquire the numeral roots of nonlinear boundary value problems(BVPs) of 14th-order utilizing cubic splines. Two cubic splines; Polynomial and non-polynomial, are exploited to find out the solutions of nonlinear boundary value problems(BVPs) of 14th-order. The strategies embraced in this work depend on cubic polynomial spline(CPS) and cubic non-polynomial spline(CNPS) strategy in combination of the decomposition procedure. The prescribed method transforms the boundary value problem to a system of linear equations. The algorithms we are going to develop in this paper are not only simply the approximation solution of the 14th order boundary value problems using cubic polynomial spline(CPS) and cubic non-polynomial spline(CNPS) but also describe the estimated derivatives of 1st order to 14th order of the analytic solution at the same time. These strategies will be operated on three problems to evidence the handiness of the technique by means of step size h = 1/5. The exactness of this method for detailed investigation is equated with the precise solution and conveyed through tables. To reveal the efficiency of our outcomes, the AEs (absolute errors) of the CPS and CNPS have been contrasted with Adomian Decomposition Method and Differential Transform Method and our results discovered to be more precise.

Keywords

• Boundary value problems
• Cubic spline
• Absolute errors
• Central finite difference approximations