Stefan M. Filipov

TL;DR: In this article, the authors presented a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations, which works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem solution; then, the end value of the solution is used in a simple iteration formula to correct the original condition; the process is repeated until the second boundary condition is satisfied.

TL;DR: A novel shooting method for solving two-point boundary value problems for second order ordinary differential equations using an auxiliary function that satisfies both boundary conditions and minimizes the H1 semi-norm of the difference between itself and the initial value problem solution.

TL;DR: It is proved that using finite differences to discretize the sequence of linear differential equations arising from quasi-linearization leads to the usual iteration formula of the Newton finite difference method, and a way of replacing the Newton, Picard, and constant-slope finite difference methods by respective successive application of the linear shooting method is proposed.

TL;DR: The use of the simple shooting-projection method for solving two-point boundary value problems for second-order ordinary integro-differential equations is proposed.

TL;DR: In this paper, the authors considered one-dimensional heat transfer in a media with temperature-dependent thermal conductivity, and solved numerically the one dimensional unsteady heat conduction equation with certain initial and boundary conditions.