Related papers: Use of Homotopy Perturbation Method for Solving Mu…
In this paper, the fractional-order Burgers-Poisson equation is introduced by replacing the first-order time derivative by fractional derivative of order $\alpha$. Both exact and approximate explicit solutions are obtained by employing…
Using standard calculus, explicit formulas for one-, two- and three-dimensional homotopy operators are presented. A derivation of the one-dimensional homotopy operator is given. A similar methodology can be used to derive the…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
Using critical point theory methods we undertake the existence and multiplicity of solutions for discrete anisotropic two-point boundary value problems.
This article develops a new predictor-corrector algorithm for numerical path tracking in the context of polynomial homotopy continuation. In the corrector step it uses a newly developed Newton corrector algorithm which rejects an initial…
We present a new view onto the successive approximations' approach in study of the two-point nonlinear fractional boundary value problems. In order to reduce the original problem and further construct its approximate solution we use the…
The manuscript addresses the problem of finding all solutions of power flow equations or other similar nonlinear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly in the…
This paper presents a Laguerre homotopy method for optimal control problems in semi-infinite intervals (LaHOC), with particular interests given to nonlinear interconnected large-scale dynamic systems. In LaHOC, spectral homotopy analysis…
Systems of polynomial equations arise frequently in computer vision, especially in multiview geometry problems. Traditional methods for solving these systems typically aim to eliminate variables to reach a univariate polynomial, e.g., a…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
This article studies the existence of long-time solutions to the Hamiltonian boundary value problem, and their consistent numerical approximation. Such a boundary value problem is, for example, common in Molecular Dynamics, where one aims…
Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector…
Large-scale strongly nonlinear and nonconvex mixed-integer nonlinear programming (MINLP) models frequently appear in optimisation-based process synthesis, integration, intensification, and process control. However, they are usually…
First order shape optimization methods, in general, require a large number of iterations until they reach a locally optimal design. While higher order methods can significantly reduce the number of iterations, they exhibit only local…
In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…
In this paper, a full (nested) multigrid scheme is proposed to solve eigenvalue problems. The idea here is to use the multilevel correction method to transform the solution of eigenvalue problem to a series of solutions of the corresponding…
In this paper, we perform a comparison study of two methods (the embedded boundary method and several versions of the mixed finite element method) to solve an elliptic boundary value problem.
We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…
This paper presents an adaptive multiple-shooting method to solve stochastic multi-point boundary value problems. The heuristic to choose the shooting points is based on separating the effects of drift and diffusion terms and comparing the…
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…