Related papers: Efficient implementation of RKN-type Fourier collo…

The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…

In this paper, a recently published method [Hussain, Ismail, Senua, Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method, J. Comput. Appl. Math. 306 (2016) 179-199] for solving fourth-order…

We investigate and derive second solutions to linear homogeneous second-order difference equations using a variety of methods, in each case going beyond the purely formal solution and giving explicit expressions for the second solution. We…

We consider a Urysohn integral operator $\mathcal{K}$ with kernel of the type of Green's function. For $r \geq 1$, a space of piecewise polynomials of degree $\leq r-1 $ with respect to a uniform partition is chosen to be the approximating…

In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…

This paper proposes a strong second-order two-step explicit/implicit technique with spectral orthogonal basis Galerkin finite element method for solving a two-dimensional Gray-Scott model subject to appropriate initial and boundary…

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…

We present a set of new, efficient high-order symplectic methods designed for Hamiltonian systems with cubic or quartic potentials. By demonstrating that polynomial potentials require fewer order conditions, we develop schemes that…

Our paper "Solving Third Order Linear Difference Equations in Terms of Second Order Equations" gave two algorithms for solving difference equations in terms of lower order equations: an algorithm for absolute factorization, and an algorithm…

Dual descent methods are commonly used to solve network flow optimization problems, since their implementation can be distributed over the network. These algorithms, however, often exhibit slow convergence rates. Approximate Newton methods…

In this paper we construct high order numerical methods for solving third and fourth orders nonlinear functional differential equations (FDE). They are based on the discretization of iterative methods on continuous level with the use of the…

In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…

We develop a robust solver for a second order mixed finite element splitting scheme for the Cahn-Hilliard equation. This work is an extension of our previous work in which we developed a robust solver for a first order mixed finite element…

In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…

Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit…

When integrating the radiative transfer equation for polarized light, the necessity of high-order numerical methods is well known. In fact, well-performing high-order formal solvers enable higher accuracy and the use of coarser spatial…

Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and…

The present paper continues our investigation of an implementation of a least-squares collocation method for higher-index differential-algebraic equations. In earlier papers, we were able to substantiate the choice of basis functions and…

In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\"odinger-type,…

In this paper, we propose a distributed second- order method for reinforcement learning. Our approach is the fastest in literature so-far as it outperforms state-of-the-art methods, including ADMM, by significant margins. We achieve this by…