Parametric spline method for a class of singular two-point boundary value problems

A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method

“…The function g(u) represents the heat generation within the solid, u is the temperature and the constant p is equal to 0, 1 or 2 depending on whether the solid is a plate, a cylinder or a sphere [4]. In recent years, an increasing interest has been observed in investigating singular two-point boundary value problems and a number of methods have been proposed, see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Although these numerical methods have many advantages, a huge amount of computational work is required for getting accurate approximations, especially for nonlinear problems.…”

Spline Approximate Solutions of Arbitrary Order Linear Boundary Value Problems

“…t ∈ [0, 3 2 ], N = 180 Example 4. For t ∈ [−1, 1], consider the following boundary value problem [11] (1) (1) = 2 e −1 − 2 e, x (2) (−1) + x (2) (1) = 2 e −1 − 6 e, x (3) (−1) + x (3) (1) = −12 e, x (4) (−1) + x (4) (1) = −4 e −1 − 20 e, x (5) (−1) + x (5) (1) = −10 e −1 − 30 e, x (6) (−1) + x (6) (1) = −18 e −1 − 42 e, x (7) (−1) + x (7) (1) = −28 e −1 − 56 e.…”

“…In 1970s, Scott and Watts [1] described the numerical solution of linear boundary value problems (BVP) using a combination of superposition and orthonormalization. Recently, there are a plenty of methods for the numerical solutions of linear BVP of different orders, such as finite difference methods [2], [3], splines [4], [5], parametric splines [6], [7] and so on. In [8], Lian and Lin consider nth order initial value problems.…”

Methods for solving singular boundary value problems using splines: a review

“…The numerical method is tested for its efficiency by considering two examples from physiology. In [54], J. Rashidinia, Z. Mahmoodi and M. Ghasemi present a three point finite difference method based on uniform mesh using parametric spline for the class of singular two-point BVPs…”