Sinc-Collocation Method for Solving Linear and Nonlinear System of Second-Order Boundary Value Problems

Abstract

Sinc methods are now recognized as an efficient numerical method for problems whose solutions may have singularities, or infinite domains, or boundary layers. This work deals with the sinc-collocation method for solving linear and nonlinear system of second order differential equation. The method is then tested on linear and nonlinear examples and a comparison with B-spline method is made. It is shown that the sinc-collocation method yields better results.

A Family of Boundary Value Methods for Systems of Second-Order Boundary Value Problems

“…Comparisons are made between the BVM = 4 and the ETRs [5] as well as between the BVM = 8 and the TOMs [5] by obtaining the maximum errors in the interval of integration. We also compared our methods with the Sinc-Collocation method [20]. Examples 6 and 7 were solved using the BVMs of order 6.…”

Extended cubic B-spline method for solving a system of non-linear second-order boundary value problems

“…Various approximate methods have been developed and these include He's homotopy perturbation method [25], Laplace homotopy analysis method [23], variational iteration method [21], homotopy perturbation-reproducing kernel method [14], reproducing kernel method [13], sinc-collocation method [11,12], local radial basis function based differential quadrature [10], Chebyshev finite difference [26], continuous genetic algorithm [2], modified homotopy analysis method [5], three positive solution method [19], spline collocation approach [20], cubic B-spline scaling functions [9], Chebyshev wavelet finite difference [22], B-spline method [6], multidimensional triangular models [16], multistage optimal homotopy asymptotic method [3,4], and hybrid cubic B-spline method [18]. The extended cubic B-spline was first proposed by Han and Liu in 2003 [27].…”

Error analysis of sinc-Galerkin method for time-dependent partial differential equations

“…Particular examples include Euler-Bernoulli beam problems [3], elliptic problems [2], Poisson-like problems [28], inverse problem [22], dynamic elasto-plastic problem [1], the generalized regularized long wave(GRLW) equation [19], integral equation [17,18], system of second-order differential equation [7], Sturm-Liouville problems [4], higher-order differential equation [5,21], multiple space dimensions [16], Troesch's problem [6], clamped plate eigenvalue problem [10], biharmonic problems [11], and fourth-order parabolic equation [12].…”