Using the Theory of Functional Connections to Solve Boundary Value Geodesic Problems

A numerical approach to solve eighth order boundary value problems by Haar wavelet collocation method

In this paper a robust and accurate algorithm based on Haar wavelet collocation method (HWCM) is proposed for solving eighth order boundary value problems. We used the Haar direct method for calculating multiple integrals of Haar functions. To illustrate the efficiency and accuracy of the concerned method, few examples are considered which arise in the mathematical modeling of fluid dynamics an...

A New Meshless Method to Solve Boundary-value Problems

This paper presents a new family of meshless methods for the solution of boundary-value problems. In the h-p cloud method, the solution space is composed of radial basis functions associated with a set of nodes arbitrarily placed in the domain. The paper describes the construction of the h-p cloud functions using a signed partition of unity and how h, p or h-p reenements can be implemented with...

Spectral Theory of Boundary Value Problems

Functional Boundary Value Problems without Growth Restrictions

Let J = [O,TJ and F : C°(J) x C°(J) x lH'.--7 Ll(J) be an operator. Existence theorems for the functional differential equation (g(x'(t)))' = (F(x,x',x'(t)))(t) with functional boundary conditions generalizing the non-homogeneous Dirichlet boundary conditions and nonhomogeneous mixed boundary conditions are given. Existence results are proved by the Leray-Schauder degree theory under some sign ...

Application of Decoupled Scaled Boundary Finite Element Method to Solve Eigenvalue Helmholtz Problems (Research Note)

A novel element with arbitrary domain shape by using decoupled scaled boundary finite element (DSBFEM) is proposed for eigenvalue analysis of 2D vibrating rods with different boundary conditions. Within the proposed element scheme, the mode shapes of vibrating rods with variable boundary conditions are modelled and results are plotted. All possible conditions for the rods ends are incorporated ...