Boundary value problems arise in many applications, and shooting methods are one approach to approximate the solution of such problems. A Shooting method transforms a boundary value problem into a sequence of initial value problems, and takes the advantage of the speed and adaptivity of initial value problem solvers. The implementation of continuous Runge-Kutta methods with defect control for i...

Bordered almost block diagonal systems arise from discretizing a linearized rst-order system of n ordinary diierential equations in a two-point boundary value problem with non-separated boundary conditions. The discretization may use spline collocation, nite diierences, or multiple shooting. After internal condensation, if necessary, the bordered almost block diagonal system reduces to a standa...

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

in this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. the numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. in order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

In this paper, numerical solution of two points 2 order nonlinear boundary-value problems was considered. The numerical solution was reviewed with nonlinear shooting method, finite-difference method and fourth order compact method. The results were compared to check the accuracy of numerical schemes with exact solution. It was found that the nonlinear shooting method is more accurate than finit...

The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP). In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,R). Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can i...