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The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…

Numerical Analysis · Mathematics 2021-08-26 Junyang Wang , Jon Cockayne , Oksana Chkrebtii , T. J. Sullivan , Chris. J. Oates

In this study, perturbation-iteration algorithm, namely PIA, is applied to solve some types of system of fractional differential equations (FDEs) for the first time. To illustrate the efficiency of the method, numerical solutions are…

Numerical Analysis · Mathematics 2016-07-29 Mehmet Senol , I. T. Dolapci

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

Numerical Analysis · Mathematics 2020-02-11 Toby Sanders , Rodrigo B. Platte , Robert D. Skeel

We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…

Functional Analysis · Mathematics 2017-01-20 K. R. Kazmi , Mohd Furkan

In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…

Statistical Mechanics · Physics 2025-12-30 Jiri Hoogland , Dimitri Neumann

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

Analysis of PDEs · Mathematics 2020-09-04 Prakash Kumar Das , M. M. Panja

A new approach for integration of the initial value problem for ordinary differential equations is suggested. The algorithm is based on approximation of the solution by a system of functions that contains orthogonal exponential polynomials.

Numerical Analysis · Mathematics 2011-05-10 Vladimir S. Chelyshkov

Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical…

Machine Learning · Computer Science 2023-09-01 Marc Finzi , Andres Potapczynski , Matthew Choptuik , Andrew Gordon Wilson

We discuss existence, non-uniqueness and regularity of one- and two-sided solutions of initial value problems for scalar quasi-linear ordinary differential equations where the initial condition corresponds to an impasse point of the…

Dynamical Systems · Mathematics 2020-08-24 Werner M. Seiler , Matthias Seiss

In this work we study Lie symmetry analysis of initial and boundary value problems for partial differential equations (PDE) with Caputo fractional derivative. We give generalized definition and theorem for the symmetry method for PDE with…

Analysis of PDEs · Mathematics 2020-03-18 Gulistan Iskenderoglu , Dogan Kaya

The issue of inheriting periodicity of an exact solution of a dynamic system by a difference scheme is considered. It is shown that some difference schemes (midpoint scheme, Kahan scheme) in some special cases provide approximate solutions…

Classical Analysis and ODEs · Mathematics 2024-12-03 Wang Shiwei , Alexander Zorin , Marina Konyaeva , Mikhail Malykh , Leonid Sevastianov

Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.

Optimization and Control · Mathematics 2011-12-06 Sébastien Marinesque

Given an argumentation network with initial values to the arguments, we look for algorithms which can yield extensions compatible with such initial values. We find that the best way of tackling this problem is to offer an iteration formula…

Artificial Intelligence · Computer Science 2015-03-19 D. Gabbay , O. Rodrigues

In this paper, within scaling invariance theory, we define and apply to the numerical solution of a similarity boundary layer model an iterative transformation method. The boundary value problem to be solved depends on a parameter and is…

Numerical Analysis · Mathematics 2020-11-20 Riccardo Fazio

Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…

Functional Analysis · Mathematics 2026-01-12 Nida Izhar Mallick , Izhar Uddin

A new Hamilton principle of convolutional type, completely compatible with the initial conditions of an IVP, has been proposed in a recent publication arXiv:1912.08490v1 [math-ph]. In the present paper the possible use of this principle for…

Numerical Analysis · Mathematics 2020-11-24 Vassilios K. Kalpakides

In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…

Numerical Analysis · Mathematics 2024-12-20 Raimondas Ciegis , Petr Vabishchevich

In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using projection method, we propose an iterative algorithm for the system of split variational inequality problems. Further, we prove that…

Functional Analysis · Mathematics 2014-08-19 Kaleem Raza Kazmi

A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic…

Numerical Analysis · Mathematics 2021-03-17 Feng Bao , Yanzhao Cao , He Zhang

In this paper, we first establish the convergence criteria of the residual iteration method for solving quadratic eigenvalue problem- s. We analyze the impact of shift point and the subspace expansion on the convergence of this method. In…

Numerical Analysis · Mathematics 2017-01-12 Liu Yang , Yuquan Sun , Fanghui Gong