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• Open Access

ARTICLE

Coupled ABC and Spline Collocation Approach for a Class of Nonlinear Boundary Value Problems over Semi-Infinite Domains

S.A. Khuri1, A. Sayfy1
CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 81-96, 2014, DOI:10.3970/cmes.2014.101.081
Abstract In this article, we introduce a numerical scheme to solve a class of nonlinear two-point BVPs on a semi-infinite domain that arise in engineering applications and the physical sciences. The strategy is based on replacing the boundary condition at infinity by an asymptotic boundary condition (ABC) specified over a finite interval that approaches the given value at infinity. Then, the problem complimented with the resulting ABC is solved using a fourth order spline collocation approach constructed over uniform meshes on the truncated domain. A number of test examples are considered to confirm the accuracy, efficient treatment of the boundary condition… More >

• Open Access

ARTICLE

Legendre Polynomials Method for Solving a Class of Variable Order Fractional Differential Equation

Lifeng Wang1, Yunpeng Ma1,2, Yongqiang Yang1
CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 97-111, 2014, DOI:10.3970/cmes.2014.101.097
Abstract In this paper, a numerical method based on the Legendre polynomials is presented for a class of variable order fractional differential equation. We adopt the Coimbra variable order fractional operator, which can be viewed as a Caputo-type definition. Three different kinds of operational matrixes with Legendre polynomials are derived. A truncated the Legendre polynomials series together with the products of several dependent matrixes are utilized to reduce the variable order fractional differential equation to a system of algebraic equations. The solution of this system gives the approximation solution for the truncated limited n. An error analysis technique is also given.… More >

• Open Access

ARTICLE

A Meshless Method for Solving the 2D Brusselator Reaction-Diffusion System

M. Mohammadi1, R. Mokhtari2,3, R. Schaback4
CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 113-138, 2014, DOI:10.3970/cmes.2014.101.113
Abstract In this paper, the two-dimensional (2D) Brusselator reaction-diffusion system is simulated numerically by the method of lines. The proposed method is implemented as a meshless method based on spatial trial functions in the reproducing kernel Hilbert spaces. For efficiency and stability reasons, we use the Newton basis introduced recently by Müller and Schaback. The method is shown to work in all interesting situations described by Hopf bifurcations and Turing patterns. More >

• Open Access

ARTICLE

Prediction of Fracture Parameters of High Strength and Ultra-high Strength Concrete Beam using Gaussian Process Regression and Least Squares

Shantaram Parab1, Shreya Srivastava2, Pijush Samui3, A. Ramachandra Murthy4
CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 139-158, 2014, DOI:10.3970/cmes.2014.101.139
Abstract This paper studies the applicability of Gaussian Process Regression (GPR) and Least Squares Support Vector Machines (LSSVM) to predict fracture parameters and failure load (Pmax) of high strength and ultra-high strength concrete beams. Fracture characteristics include fracture energy (GF), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODC) Mathematical models have been developed in the form of relation between several input variables such as beam dimensions, water cement ratio, compressive strength, split tensile strength, notch depth, modulus of elasticity and output fracture parameters. Four GPR and four LSSVM models have been developed using MATLAB software for training… More >   