Related papers: Analytic solution of system of singular nonlinear …
We present an algorithm for determining the minimal order differential equations associated to a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted…
In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general…
One of the main objectives of science is the recognition of a general pattern in a particular phenomenon in some particular regime. In this work, this is achieved with the analytical expression for the optimal protocol that minimizes the…
We present a comprehensive study for common second order PDE's in two dimensional disk-like systems and show how their solution can be approximated by finding the Green function of an effective one dimensional system. After elaborating on…
We show how to solve initial-boundary value problems for integrable nonlinear differential-difference equations on a finite set of integers. The method we employ is the discrete analogue of the unified transform (Fokas method). The…
Consider the following Lane-Emden system with Dirichlet boundary conditions: \[ -\Delta U = |V|^{\beta-1}V,\ -\Delta V = |U|^{\alpha-1}U \text{ in }\Omega,\qquad U=V= 0 \text{ on }\partial \Omega, \] in a bounded domain $\Omega$, for…
An implementation and an application of the combination of the genetic algorithm and Newton's method for solving a system of nonlinear equations is presented. The method first uses the advantage of the robustness of the genetic algorithm…
We introduce a two-phase approximation method designed to resolve singularities in three-dimensional harmonic Dirichlet problems. The approach utilizes the classical Green's function representation, decomposing the function into its…
We prove convergence for the nonoverlapping Robin-Robin method applied to nonlinear elliptic equations with a $p$-structure, including degenerate diffusion equations governed by the $p$-Laplacian. This nonoverlapping domain decomposition is…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…
A central tool in the study of systems of linear equations with integer coefficients is the Generalised von Neumann Theorem of Green and Tao. This theorem reduces the task of counting the weighted solutions of these equations to that of…
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features an adaptive choice of the damping parameter in the Newton…
Linear-time invariant (LTI) oscillation systems such as forced mechanical vibration, series RLC and parallel RLC circuits can be solved by using simplest initial conditions or employing of Green's function of which knowledge of initial…
This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly…
Atkinson developed a strategy which splits solution of a PDE system into homogeneous and particular solutions, where the former have to satisfy the boundary and governing equation, while the latter only need to satisfy the governing…
Isolating the singularity in the Green's function solution of the inhomogeneous, differential equation for the Stermheimer function of a layered electron gas, permits the construction of an approximate solution of the Stermheimer function…
In this paper we develop a Neumann-Neumann type domain decomposition method for elliptic problems on metric graphs. We describe the iteration in the continuous and discrete setting and rewrite the latter as a preconditioner for the Schur…
In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a variable stepsize which is updated at each iteration and based on some previous…
The well-known expressions for the Green's functions for the Helmholtz equation in polar coordinates with Dirichlet and Neumann boundary conditions are transformed. The slowly converging double series describing these Green's functions are…