An Explicit Time Integration Scheme Based on B-Spline Interpolation and Its Application in Wave Propagation Analysis

Abstract

An explicit time integration scheme for hyperbolic equations is proposed using B-spline interpolation and weighted residual method. It has simple formulation and calculation procedure. With one adjustable algorithmic parameter, new scheme has higher accuracy when compared with other excellent explicit schemes. New scheme has controllable and also desirable period elongation which is verified by theoretical analysis and numerical simulations. Especially, a demonstrative dispersion analysis coupled with the corresponding wave propagation demonstrate the desirable numerical dissipation property and the effectiveness of the proposed scheme for wave propagation problems.