The Sinc-Galerkin method for fourth-order differential equations
SIAM Journal on Numerical Analysis
Sinc methods for quadrature and differential equations
Sinc methods for quadrature and differential equations
Numerical methods for special nonlinear boundary-value problems of order 2m
Journal of Computational and Applied Mathematics
A comparison between Adomian decomposition method and Taylor series method in the series solutions
Applied Mathematics and Computation
Quartic spline method for solving fourth order obstacle boundary value problems
Journal of Computational and Applied Mathematics
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In this paper, we present efficient numerical algorithms for the approximate solution of nonlinear fourth-order boundary value problems. The first algorithm deals with the sinc-Galerkin method (SGM). The sinc basis functions prove to handle well singularities in the problem. The resulting SGM discrete system is carefully developed. The second method, the Adomian decomposition method (ADM), gives the solution in the form of a series solution. A modified form of the ADM based on the use of the Laplace transform is also presented. We refer to this method as the Laplace Adomian decomposition technique (LADT). The proposed LADT can make the Adomian series solution convergent in the Laplace domain, when the ADM series solution diverges in the space domain. A number of examples are considered to investigate the reliability and efficiency of each method. Numerical results show that the sinc-Galerkin method is more reliable and more accurate.