Application of Liapunov Theory to Boundary Value Problems. II

Extension of Liapunov Theory to Five-point Boundary Value Problems for Third Order Differential Equations

This paper presents criteria for the existence and uniqueness of solutions to five-point boundary value problems associated with third order differential equations by using matching technique. ’Liapunov-like’ functions are used as a tool to establish existence and uniqueness of solutions by matching two three-point boundary value problems. AMS Mathematics Subject Classification (2000): 34B10, 3...

Spectral Theory of Boundary Value Problems

Application of Shannon wavelet for solving boundary value problems of fractional differential equations I

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional diff<span style="font-family: NimbusRomNo...

On the Application of Geometric Singular Perturbation Theory to Some Classical Two Point Boundary Value Problems

In this tutorial, we illustrate how geometric singular perturbation theory provides a complementary dynamical systems-based approach to the method of matched asymptotic expansions for some classical singularly-perturbed boundary value problems. The central theme is that the criterion of matching corresponds to the criterion of transverse intersection of manifolds of solutions. This theme is stu...

Wavelet Approximations on Closed Surfaces and Their Application to Boundary-value Problems of Potential Theory

Wavelets on closed surfaces in Euclidean space R 3 are introduced starting from a scale discrete wavelet transform for potentials harmonic down to a spherical boundary. Essential tools for approximation are integration formulas relating an integral over the sphere to suitable linear combinations of function values (resp. normal derivatives) on the closed surface under consideration. A scale dis...