A discrete Taylor series method for the solution of two-point boundary-value problems

A method for solving ordinary differential equations of the two-point boundary-value problems (TPBVP) is presented. The ordinary differential equations of the TPBVP are reduced to linear integral equations. The solution to the linear integral equation reformulation is expanded in the discrete Taylor series and a Gauss-quadrature integration rule is provided for approximating definite integrals. Application of this method results in the transformation of the integral equations into a linear system of algebraic equations in the Taylor coefficients. Illustrative examples are included to demonstrate the validity and applicability of the proposed method.