Indian Journal of Science and Technology

Abstract

Objective: A higher order numerical scheme for two-point boundary interface problem with Dirichlet and Neumann boundary condition on two different sides is propounded. Methods: Orthogonal cubic spline collocation techniques have been used (OSC) for the two-point interface boundary value problem. To approximate the solution a piecewise Hermite cubic basis functions have been used. Findings: Remarkable features of the OSC are accounted for the numerous applications, theoretical clarity, and convenient execution. The stability and efficiency of orthogonal spline collocation methods over B-splines have made the former more preferable than the latter. As against finite element methods, determining the approximate solution and the coefficients of stiffness matrices and mass is relatively fast as the evaluation of integrals is not a requirement. The systematic incorporation of boundary and interface conditions in OSC adds to the list of advantages of preferring this method. Novelty: As against the existing methodologies it becomes clear from our findings that OSC is dominantly computationally superior. A computational treatment has been implemented on the two-point interface boundary value problem with super-convergent results of derivative at the nodal points, being the noteworthy finding of the study.

Keywords: Helmholtz problem; Orthogonal spline collocation techniques (OSC); Discontinuous data; Super Convergence; Piecewise cubic Hermite basis functions; Almost block diagonal (ABD) structure