An Accurate Numerical Algorithm for Solving Singular and Nonsingular System of Initial Value Problems on Large Interval

Extended cubic B-spline method for solving a system of non-linear second-order boundary value problems

“…Various approximate methods have been developed and these include He's homotopy perturbation method [25], Laplace homotopy analysis method [23], variational iteration method [21], homotopy perturbation-reproducing kernel method [14], reproducing kernel method [13], sinc-collocation method [11,12], local radial basis function based differential quadrature [10], Chebyshev finite difference [26], continuous genetic algorithm [2], modified homotopy analysis method [5], three positive solution method [19], spline collocation approach [20], cubic B-spline scaling functions [9], Chebyshev wavelet finite difference [22], B-spline method [6], multidimensional triangular models [16], multistage optimal homotopy asymptotic method [3,4], and hybrid cubic B-spline method [18]. The extended cubic B-spline was first proposed by Han and Liu in 2003 [27].…”