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
International Journal of Computer Mathematics
A recent survey on computational techniques for solving singularly perturbed boundary value problems
International Journal of Computer Mathematics
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Singularly perturbed boundary value problems (BVPs) for fourth order ordinary differential equations (ODEs) with a small positive parameter multiplying the highest derivative of the form -εyiυ(x) - a(x)y'''(x) + b(x)y''(x) - c(x)y(x) = -f(x), x ∈ D := (0, 1), y(0)=p, y(1)=q, y''(0)= -r, y''(1)= -s, are considered. The given fourth order BVP is transformed into a system of weakly coupled system of two second order ODEs, one without the parameter and the other with the parameter ε multiplying the highest derivative, and suitable boundary conditions. In this paper computational methods for solving this system are presented. In these methods we first find the zero order asymptotic approximation expansion of the solution of the weakly coupled system. Then the system is decoupled by replacing the first component of the solution by its zero order asymptotic approximation expansion of the solution in the second equation. Then the second equation is solved by the fitted operator method (FOM), fitted mesh method (FMM) and boundary value technique (BVT). Error estimates are derived and examples are provided to illustrate the methods.