Related papers: The method of solving a scalar initial value probl…
We suggest a modification of the operator exponential method for the numerical solving the difference linear initial boundary value problems. The scheme is based on the representation of the difference operator for given boundary conditions…
Many Engineering Problems could be mathematically described by Final Value Problem, which is the inverse problem of Initial Value Problem. Accordingly, the paper studies the final value problem in the field of ODE problems and analyses the…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
A new method for finding first integrals of discrete equations is presented. It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) formulation. The method is based on a newly established…
Various traditional numerical methods for solving initial value problems of differential equations often produce local solutions near the initial value point, despite the problems having larger interval solutions. Even current popular…
A variable stepsize exponential multistep integrator, with contour integral approximation of the operator-valued exponential functions, is proposed for solving semilinear parabolic equations with nonsmooth initial data. By this approach,…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
When one wishes to numerically solve an initial value problem, it is customary to rewrite it as an equivalent first-order system to which a method, usually from the class of Runge-Kutta methods, is applied. Directly treating higher-order…
We established a new eighth-order iterative method, consisting of three steps, for solving nonlinear equations. Per iteration the method requires four evaluations (three function evaluations and one evaluation of the first derivative).…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…
A method based on order completion for solving general equations is presented. In particular, this method can be used for solving large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems.
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
Chen and Hsiao gave the numerical solution of initial value problems of systems of linear differential equations with constant coefficients by Walsh polynomials approach. This result was improved by G\'at and Toledo for initial value…
Implicit methods for the numerical solution of initial-value problems may admit multiple solutions at any given time step. Accordingly, their nonlinear solvers may converge to any of these solutions. Below a critical timestep, exactly one…
Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-Kutta methods. We generalize this approach to multistep…
An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction $A + A \rightarrow\varnothing$ modeling is discussed. Finite difference method together with the linear…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…