Related papers: Variational Iteration Homotopy Perturbation Method…
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is…
This paper presents a new method for solving a class of nonlinear optimal control problems with a quadratic performance index. In this method, first the original optimal control problem is transformed into a nonlinear two-point boundary…
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…
In this paper we discuss a recent application of a variational homotopy perturbation method to rather simple nonlinear oscillators . We show that the main equations are inconsistent and for that reason the results may be of scarce utility.
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…
This paper presents a new and straightforward procedure for solving bilinear quadratic optimal control problem. In this method, first the original optimal control problem is transformed into a nonlinear twopoint boundary value problem…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for the start solutions of a homotopy via the function which…
Computing accurate periodic responses in strongly nonlinear or even non-smooth vibration systems remains a fundamental challenge in nonlinear dynamics. Existing numerical methods, such as the Harmonic Balance Method (HBM) and the Shooting…
The paper considers the integral Volterra equations of the first kind which are related to the inverse boundary-value heat conduction problem. The algorithms have been developed to numerically solve the respective integral equations, which…
Recently, the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs), has been proposed for the efficient solution of Hamiltonian problems, as well as for other types of conservative problems. In…
A simple third order compact finite element method is proposed for one-dimensional Sturm-Liouville boundary value problems. The key idea is based on the interpolation error estimate, which can be related to the source term. Thus, a simple…
We propose a new model reduction technique for multiscale scalar transport problems that exhibit dominant axial dynamics. To this aim, we rely on the separation of variables to combine a Hierarchical Model (HiMod) reduction with a two-scale…
Differential equations have void applications in several practical situations, sciences, and non sciences as Euler Lagrange equation in classical mechanics, Radioactive decay in nuclear physics, Navier Stokes equations in fluid dynamics,…
The paper presents a variational quantum algorithm to solve initial-boundary value problems described by second-order partial differential equations. The approach uses hybrid classical/quantum hardware that is well suited for quantum…
Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
In this paper a special type of difference equations is investigated. The impulses start abruptly at some points and their action continue on given finite intervals. This type of equations is used to model a real process. An algorithm,…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…