Numerical Solution of Troesch’s Problem by Sinc-Collocation Method

Abstract

A new algorithm is presented for solving Troesch's problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical experiments are made. Compared with the modified homotopy perturbation technique (MHP), the variational iteration method and the Adomian decomposition method. It is shown that the sinc-collocation method yields better results.

Novel efficient collocation method for Sturm–Liouville problems with nonlocal integral boundary conditions

“…Sinc methods were developed by Frank Stenger (the pioneer of this field), members in this school, El-Gamel with his students and others [12][13][14][15]. Sinc methods were used for solving a wide range of linear and nonlinear problems arising from scientific and engineering applications including Blasius equation [16], Hallens integral equation [17], inverse problem [18], oceanographic problems with boundary layers [19], Troeschs problem [20]and the fourth-order parabolic equation [21]. Very recently, El-Gamel used the sinc procedure to solve time-dependent partial differential equations and the clamped plate eigenvalue problem [22,23] and Babaei et al developed the sinc spectral collocation technique for time-fractional multi-dimensional partial integro-differential equation [24].…”

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].…”

Laguerre wavelet method for solving Troesch equation

“…In literature, several numerical methods have been employed to solve this nonlinear problem. We can list these methods as: Finite difference method [1], Chebyshev wavelet method [2], Chebysev collocation method [3], A finite-element approach based on cubic B-spline collocation [4], An accurate asymptotic approximation [5], Adomian decomposition method and the reproducing kernel method [6], Christov rational functions [7], Decomposition method [8], Differential transform method [9], High-Order Difference Schemes [10], Homotopy perturbation method [11], Hybrid heuristic computing [12], Jacobi-Gauss collocation method [13], Laplace transform and a modified decomposition technique [14], Modified Homotopy perturbation method [15], Newton-Raphson-Kantorovich approximation method [16], Optimal Homotopy asymptotic method [17], Perturbation Method and Laplace-Padé Approximation [18], Scott and the Kagiwada-Kalaba algorithms [19], Modified nonlinear Shooting method [20], Sinc-Collocation Method [21], sinc-Galerkin method [22], Variational iteration method [23,24].…”