Related papers: Solution of nonlinear system of equations through …
The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian…
We consider systems of nonlinear magnetostatics and quasistatics that typically arise in the modeling and simulation of electric machines. The nonlinear problems, eventually obtained after time discretization, are usually solved by…
This paper proposes a volumetric penalty method to simulate the boundary conditions for a non-linear hyperbolic problem. The boundary conditions are assumed to be maximally strictly dissipative on a non-characteristic boundary. This…
The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence…
We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.
We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence)…
By setting up appropriate uniform convergence structures, we are able to reformulate the Order Completion Method of Oberguggenberger and Rosinger in a setting that more closely resembles the usual topological constructions for solving PDEs.…
The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…
The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of…
In this paper we propose and analyze three parallel hybrid extragradient methods for finding a common element of the set of solutions of equilibrium problems involving pseudomonotone bifunctions and the set of fixed points of nonexpansive…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot…
In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with…
In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.
We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs,to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium…
Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
Nonlinear two-point boundary value problems arise in numerous areas of application. The existence and number of solutions for various cases has been studied from a theoretical standpoint. These results generally rely upon growth conditions…