Approximate method for the numerical solution of singular perturbation problems
Applied Mathematics and Computation
Numerical solution of singular perturbation problems via deviation arguments
Applied Mathematics and Computation
Numerical treatment of singularity perturbed two point boundary value problems
Applied Mathematics and Computation
Singular perturbation methods for ordinary differential equations
Singular perturbation methods for ordinary differential equations
A computational method for solving singular perturbation problems
Applied Mathematics and Computation
Applied Mathematics and Computation
Applied Mathematics and Computation
Applied Mathematics and Computation
Upper and lower solution method for fourth-order four-point boundary value problems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A recent survey on computational techniques for solving singularly perturbed boundary value problems
International Journal of Computer Mathematics
International Journal of Computer Mathematics
Neural, Parallel & Scientific Computations
Computers & Mathematics with Applications
Mathematical and Computer Modelling: An International Journal
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Singularly perturbed two-point boundary value problems (BVPs) for fourth-order ordinary differential equations (ODEs) with a small positive parameter multiplying the highest derivative are considered. A numerical method is suggested in this paper to solve such problems. In this method, the given BVP is transformed into a system of two ODEs subject to suitable boundary conditions. Then the domain of definition of the differential equation (a closed interval) is divided into three non-overlapping sub-intervals, which we call them inner regions (boundary layers) and outer region. Then the DE is solved in these intervals separately. The solutions obtained in these regions are combined to give a solution in the entire interval. To obtain terminal boundary conditions (boundary values inside this interval) we use mostly zero-order asymptotic expansion of the solution of the BVP. First, linear equations are considered and then non-linear equations. To solve non-linear equations, Newton's method of quasi-linearization is applied. The present method is demonstrated by providing examples. The method is easy to implement and suitable for parallel computing.