A Solution of Second Kind Volterra Integral Equations Using Third Order Non-Polynomial Spline Function

In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods

A Solution of Second Kind Volterra Integral Equations Using Third Order Non-Polynomial Spline Function

In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods

A Block by Block Method for Solving System of Volterra Integral Equations with Continuous and Abel Kernels

The aim of the present paper is to introduce a block by block method for solving system of nonlinear Volterra integral equations with continuous kernels and system of Abel integral equations. We prove convergence of the method and show that its convergence order is at least six. To illustrate performance of the method, numerical experiments are presented and they are compared with HPM (Homotopy Perturbation Method) and RBFN (Radial Basis Function Network) method. The given results demonstrate remarkable ability of the proposed method

New Trends in Differential and Difference Equations and Applications

This is a reprint of articles from the Special Issue published online in the open-access journal Axioms (ISSN 2075-1680) from 2018 to 2019 (available at https://www.mdpi.com/journal/axioms/special issues/differential difference equations)

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe

Graduate school introductory computational simulation course pedagogy

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.Vita. Cataloged from PDF version of thesis.Numerical methods and algorithms have developed and matured vastly over the past three decades now that computational analysis can be performed on almost any personal computer. There is a need to be able to teach and present this material in a manner that is easy for the reader to understand and be able to go forward and use. Three popular course at MIT were without lecture notes; in this thesis the lecture notes are presented. The first chapter covers material taught in Numerical Methods for Partial Differential Equations (2.097/6.339/16.920) specifically the Integral Equation Methods section of this course, chapter two shows the notes for the course Introduction to Numerical Simulation (2.096/6.336/16.910), and chapter three contains the notes for the class Foundations of Algorithms and Computational Techniques in Systems Biology (6.581/20.482). These course notes give a broad overview of many algorithms and numerical methods that one can use to solve many problems that span many fields - from biology to aerospace to electronics to mechanics.by Laura L. Proctor.S.M

The Third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization

The third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization was held on 24-26 Sept. 1990. Sessions were on the following topics: dynamics and controls; multilevel optimization; sensitivity analysis; aerodynamic design software systems; optimization theory; analysis and design; shape optimization; vehicle components; structural optimization; aeroelasticity; artificial intelligence; multidisciplinary optimization; and composites

Mathematical Methods, Modelling and Applications

This volume deals with novel high-quality research results of a wide class of mathematical models with applications in engineering, nature, and social sciences. Analytical and numeric, deterministic and uncertain dimensions are treated. Complex and multidisciplinary models are treated, including novel techniques of obtaining observation data and pattern recognition. Among the examples of treated problems, we encounter problems in engineering, social sciences, physics, biology, and health sciences. The novelty arises with respect to the mathematical treatment of the problem. Mathematical models are built, some of them under a deterministic approach, and other ones taking into account the uncertainty of the data, deriving random models. Several resulting mathematical representations of the models are shown as equations and systems of equations of different types: difference equations, ordinary differential equations, partial differential equations, integral equations, and algebraic equations. Across the chapters of the book, a wide class of approaches can be found to solve the displayed mathematical models, from analytical to numeric techniques, such as finite difference schemes, finite volume methods, iteration schemes, and numerical integration methods

Nondifferentiable Optimization: Motivations and Applications

IIASA has been involved in research on nondifferentiable optimization since 1976. The Institute's research in this field has been very productive, leading to many important theoretical, algorithmic and applied results. Nondifferentiable optimization has now become a recognized and rapidly developing branch of mathematical programming. To continue this tradition and to review developments in this field IIASA held this Workshop in Sopron (Hungary) in September 1984. This volume contains selected papers presented at the Workshop. It is divided into four sections dealing with the following topics: (I) Concepts in Nonsmooth Analysis; (II) Multicriteria Optimization and Control Theory; (III) Algorithms and Optimization Methods; (IV) Stochastic Programming and Applications