Abstract
A family of boundary value methods (BVMs) with continuous coefficients is derived and used to obtain methods which are applied via the block unification approach. The methods obtained from these continuous BVMs are weighted the same and are used to simultaneously generate approximations to the exact solution of systems of second-order boundary value problems (BVPs) on the entire interval of integration. The convergence of the methods is analyzed. Numerical experiments were performed to show efficiency and accuracy advantages.
Highlights
We consider the general system of secondorder boundary value problems: y = f (x, y, y), x ∈ [a, b], y (a) = y0, (1)
Y (b) = yN, where f : R × R2m → Rm are continuous functions, y, y, and y ∈ Rm, and m is the dimension of the system. These second-order boundary value problems are encountered in several areas of engineering and applied sciences such as celestial mechanics, circuit theory, astrophysics, chemical kinetics, and biology
This paper is concerned with the solution of systems of second-order boundary value problems
Summary
Y (b) = yN, where f : R × R2m → Rm are continuous functions, y, y, and y ∈ Rm, and m is the dimension of the system These second-order boundary value problems are encountered in several areas of engineering and applied sciences such as celestial mechanics, circuit theory, astrophysics, chemical kinetics, and biology. In the past few decades, the boundary value methods (BVMs) have been used to solve first-order initial and boundary value problems [4,5,6,7,8] Their stability and convergence properties have been fully discussed in [5]. These BVMs are used to solve higher order initial and boundary value problems by first reducing the higher order differential equations into an equivalent first-order system.
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