This paper aims to obtain approximate solutions of the one-dimensional nonlinear Klein-Gordon equation by employing Cubic B-spline wavelets. Our scheme uses the Galerkin method and approximates the solution in the terms of cubic B-spline scaling and wavelet functions. These wavelets are applied as testing and weighting functions. Because of some properties of these wavelets such as having compa...

In this paper, an innovative neural-network architecture is proposed and elucidated. This architecture, based on the Kolmogorov's superposition theorem (1957) and called the Kolmogorov's spline network (KSN), utilizes more degrees of adaptation to data than currently used neural-network architectures (NNAs). By using cubic spline technique of approximation, both for activation and internal func...

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ball...

Implied binomial trees are constructed by fitting a risk-neutral density (in the form of ending nodal probabilities) to observed option prices. Since there are usually not enough options traded in the marketplace, a quadratic program is often used to extract the ending nodal probabilities from observed option prices. A problem with this commonly used approach is that the quadratic program is us...

A scheme to specify planar C2 Pythagorean-hodograph (PH) quintic spline curves by control polygons is proposed, in which the “ordinary” C2 cubic B-spline curve serves as a reference for the shape of the PH spline. The method facilitates intuitive and efficient constructions of open and closed PH spline curves, that typically agree closely with the corresponding cubic B-spline curves. The C2 PH ...

This paper sets a theoretical foundation for the applications of fractal interpolation functions (FIFs). We construct rational cubic spline FIFs (RCSFIFs) with quadratic denominator involving two shape parameters. The elements iterated function system (IFS) in each subinterval are identified befittingly so that graph resulting $\mathcal{C}^1$-RCSFIF lies within prescribed rectangle. These param...