A computational study of five finite element methods for the solution of a single second order linear ordinary differential equation subject to general linear, separated boundary conditions is described. In each method, the approximate solution is a piecewise polynomial expressed in terms of a B-spline basis, and is determined by solving a system of linear algebraic equations with an almost blo...

This paper investigates parallel predictor-corrector iteration schemes (PC iteration schemes) based on collocation Runge-Kutta corrector methods (RK corrector methods) with continuous output formulas for solving nonstiff initial-value problems (IVPs) for systems of first-order differential equations. The resulting parallel-iterated RK-type PC methods are also provided with continuous output for...

The von-K arm an nonlinear, dynamic, partial differential system over rectangular domains is considered, and numerically solved using both the Chebyshev-collocation and Legendre-collocation methods for the spatial discretization and the implicit Newmark-b scheme combined with a non-linear fixed point algorithm for the temporal discretization. As the system is non-linear, involving operators of ...

A popular approach for the numerical solution of boundary value ODE problems involves the use of collocation methods. Such methods can be naturally implemented so as to provide a continuous approximation to the solution over the entire problem interval. On the other hand, several authors have suggested as an alternative, certain subclasses of the implicit Runge-Kutta formulas, known as mono-imp...

The analysis and detection of edges is a central problem in applied mathematics and image processing. A number of results in recent years have shown that directional multiscale methods such as continuous curvelet and shearlet transforms offer a powerful theoretical framework to capture the geometry of edge singularities, going far beyond the capabilities of the conventional wavelet transform. T...

This paper develops a class of meshless methods that are well-suited to statistical inverse problems involving partial differential equations (PDEs). The methods discussed in this paper view the forcing term in the PDE as a random field that induces a probability distribution over the residual error of a symmetric collocation method. This construction enables the solution of challenging inverse...

In this paper, we propose a piecewise linear decision tree and its generalized form, namely the (G)PWL-DT, which introduces linearity overcomes discontinuity of existing constant trees (PWC-DT). The proposed (G)PWL-DT inherits basic topology interpretability by recursively partitioning domain into subregions, are represented leaf nodes. Rather than indicator function, employs rectifier units (R...