B-spline Method for Solving General Singularly Perturbed Boundary Value Problems Using Fitted Mesh

In this paper we develop B-spline method for solving a class of Singularly Perturbed two point boundary value problems given as

Ly = εy″ = F(x,y,y′), x ∈ (0,1) (1)

y(0) = ν₀ y(1) = ν₁, ν₀,ν₁ ∈ R (2)

We use the Fitted mesh technique to generate piecewise uniform mesh, and use B-spline method which leads to a tridiagonal linear system. In case of non-linear problems we first linearize the equation using Quasilinearization technique and the resulting problem is solved by B-spline. The convergence analysis is given and the method is shown to have uniform convergence. Numerical illustrations are given in the end to demonstrate the efficiency of our method.