B-spline method for solving linear system of second-order boundary value problems

Application of Continuous Genetic Algorithm for Nonlinear System of Second-Order Boundary Value Problems

“…Furthermore, the homotopy analysis method has been applied to solve system (1) and (2) as described in [11]. Finally, the B-spline method for solving the linear form of system (1) is proposed recently in [12]. On the other hand, the numerical solvability of other version of differential equations and other related equations can be found in [13,14,15] and references therein.…”

Sinc-Collocation Method for Solving Linear and Nonlinear System of Second-Order Boundary Value Problems

“…Maximum absolute error are tabulated in Table 2 for sinc-collocation together with the analogous results of N. Caglar and H. Caglar [3]. Example 2: [11] Now we turn to a nonlinear problem…”

“…They introduced various numerical methods. For instance, a finite difference method has been proposed in recent works [3][4][5][6][7][8]. For a nonlinear system of second-order BVPs, there are few valid methods to obtain numerical solutions.…”

A new cubic B-spline method for approximating the solution of a class of nonlinear second-order boundary value problem with two dependent variables

“…. , 5) are continuous, G 1 and G 2 are nonlinear functions of x, u, and v. For example, the iterative reproducing kernel method 3 , the variational iteration method 4 , the Chebyshev finite difference method 5 , the sinc-collocation method 6 , the homotopy perturbation method 7 , and the non-polynomial spline method 8 have been studied for (1). In addition, a combined homotopy perturbation and reproducing kernel method was also given in Ref.…”

“…10 was applicable to (1); the method in Ref. 11 was only applicable to the linear case of (1), i.e., G 1 (x, u, v) = G 2 (x, u, v) = 0; and the method in Ref. 12 was applicable to a small generalized case of (1), i.e., only including a 6 (x)u v and b 6 (x)u v as additional terms in the above system (1).…”