Related papers: Sixth-order and Seventh-order Iterative Methods fo…
The application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations is considered. Some classes of solitary wave solutions for the families of nonlinear evolution equations of fifth, sixth…
Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We…
Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…
Given a full column rank matrix $A \in \mathbb{R}^{m\times n}$ ($m\geq n$), we consider a special class of linear systems of the form $A^\top Ax=A^\top b+c$ with $x, c \in \mathbb{R}^{n}$ and $b \in \mathbb{R}^{m}$. The occurrence of $c$ in…
Iterative methods have led to better understanding and solving problems such as missing sampling, deconvolution, inverse systems, impulsive and Salt and Pepper noise removal problems. However, the challenges such as the speed of convergence…
This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…
In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…
The method of parameter variation for linear differential equations is extended to classes of second order nonlinear differential equations. This allows to reduce the latter to first order differential equations. Known classical equations…
In this paper, we propose a class of super-schemes for efficiently solving nonlinear unconstrained optimization problems. The proposed approach introduces two novel choices of step-size parameters, leading to efficient descent directions…
In this work we discuss the possibility to reduce the computational complexity of modal methods, i.e. methods based on eigenmodes expansion, from the third power to the second power of the number of eigenmodes. The proposed approach is…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
We propose a new class of rigorous methods for derivative-free optimization with the aim of delivering efficient and robust numerical performance for functions of all types, from smooth to non-smooth, and under different noise regimes. To…
In the present paper, we introduce a new family of $ \theta-$methods for solving delay differential equations. New methods are developed using a combination of decomposition technique viz. new iterative method proposed by Daftardar Gejji…
We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of…
We investigate existence of solitonic solutions for higher-order partial differential equations with polynomial nonlinearities. Using the Hirota method we obtain classification for higher-order integrable systems of equations.
The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…
In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.
We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with…
Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…
A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…