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A DualTPD method is proposed for solving nonlinear partial differential equations. The method is characterized by three main features. First, decoupling via Fenchel--Rockafellar duality is achieved, so that nonlinear terms are discretized…
We present a novel algorithm to solve a non-linear system of equations, whose solution can be interpreted as a tight lower bound on the vector of expected hitting times of a Markov chain whose transition probabilities are only partially…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…
Power Series Solution method has been used traditionally for to solve Linear Differential Equations, in Ordinary and Partial form. But this method has been limited to this kind of problems. We present the solution of problems of Non Linear…
In this article we combine the projective Landweber method, recently proposed by the authors, with Kaczmarz's method for solving systems of non-linear ill-posed equations. The underlying assumption used in this work is the tangential cone…
Fractional calculus is a powerful and effective tool for modelling nonlinear systems. The M derivative is the generalization of alternative fractional derivative. This M derivative obey the properties of integer calculus. In this paper, we…
We propose a new method for Monte Carlo solution of non-linear integral equations by combining the Newton-Kantorovich method for solving non-linear equations with the Markov Chain Monte Carlo (MCMC) method for solving linear equations. The…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
In this note we discuss the approach which was given by Wazwaz for the proof of the complete integrability to the system of nonlinear differential equations. We show that his method presented in [Wazwaz A.M. Completely integrable coupled…
The Modified Quasichemcial Model in the Distinguishable-Pair Approximation (MQMDPA) for manifold short-range orders in liquids has been successfully extended to multicomponent solutions. The extension is conducted by means of the…
This paper is presented to give numerical solutions of some cases of nonlinear wave-like equations with variable coefficients by using Reduced Differential Transform Method (RDTM). RDTM can be applied most of the physical, engineering,…
Sampling equation method is presented to look for exact solutions of nonlinear differential equations. Application of this approach to one of the extensive chaos model is considered. Exact solutions of this model in travelling wave are…
Computational methods for fractional differential equations exhibit essential instability. Even a minor modification of the coefficients or other entry data may switch good results to the divergent. The goal of this paper is to suggest the…
This paper presents the Hausdorff measure of noncompactness (MNC) within the framework of the generalized Hahn sequence space. By applying the MNC, we explore the existence of solutions for nonlinear Caputo fractional differential equations…
The matrix 2x2 spectral differential equation of the second order is considered on x in ($-\infty,+\infty$). We establish elementary Darboux transformations covariance of the problem and analyze its combinations. We select a second…
Solving quadratic systems of equations in n variables and m measurements of the form $y_i = |a^T_i x|^2$ , $i = 1, ..., m$ and $x \in R^n$ , which is also known as phase retrieval, is a hard nonconvex problem. In the case of standard…
We describe a general methods to localize any sort of k-separability and therefore also the corresponding partial entanglement in genuinely multipartite mixed quantum states. Our methods are based exclusively on the known twopartite methods…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
We present a new numerical method for solving time dependent Maxwell equations, which is also suitable for general linear hyperbolic equations. It is based on an unstructured partitioning of the spacetime domain into tent-shaped regions…