Some Problems on Variational Iteration Method

In this research project paper, I introduce some basic idea of Variational iteration method and its algorithm to solve the equations ODE & PDE, fractional differential equation, fractal differential equation and differential-difference equations. Also, some linear and nonlinear differential equations like Burger’s equation, Fisher’s equation,Wave equation and Schrodinger equation are solved by using Variational iteration method. Then I compare this method with Adomian decomposition method (ADM) and modified Variational iteration method (MVIM). The advantage of VIM, it does not require a small parameter in an equation as perturbation technique needs. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, its exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Abstract book

Welcome at the International Conference on Differential and Difference Equations & Applications 2015. The main aim of this conference is to promote, encourage, cooperate, and bring together researchers in the fields of differential and difference equations. All areas of differential & difference equations will be represented with special emphasis on applications. It will be mathematically enriching and socially exciting event. List of registered participants consists of 169 persons from 45 countries. The five-day scientific program runs from May 18 (Monday) till May 22, 2015 (Friday). It consists of invited lectures (plenary lectures and invited lectures in sections) and contributed talks in the following areas: Ordinary differential equations, Partial differential equations, Numerical methods and applications, other topics

Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]

An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u

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

Doctor of Philosophy

dissertationTrace fossils are the result of animal behaviors, such as burrowing and feeding, recorded in the rock record. Previous research has been mainly on the systematic description of trace fossils and their paleoenvironmental implications, not how animal behaviors have evolved. This study analyzes behavioral evolution using the quantification of a group of trace fossils, termed graphoglyptids. Graphoglyptids are deep marine trace fossils, typically found preserved as casts on the bottom of turbidite beds. The analytical techniques performed on the graphoglyptids include calculating fractal dimension, branching angles, and tortuosity, among other analyses, for each individual trace fossil and were performed on over 400 trace fossils, ranging from the Cambrian to the modem. These techniques were used to determine various behavioral activities of the trace makers, including feeding and behavioral evolution. Graphoglyptids have been previously identified as representing mining, grazing, farming, and/or trapping. By comparing graphoglyptids to known mining burrows and grazing trails, using fractal analysis, it was possible to rule out mining and grazing behaviors for graphoglyptids. To determine between farming and trapping, a review of all known trapping burrows was required. The hypothesis that graphoglyptids were trappers was based entirely on the hypothesized feeding behaviors of the worm Pciraonis. Close examination of Paraonis burrows indicated that the burrows are not traps. This means that, since Paraonis does not trap prey, graphoglyptids should not be considered traps either. Therefore, graphoglyptids likely represent farming behavior. This study also shows that previous interpretations of graphoglyptid behavioral evolution was far too simple. The results of the morphological analyses indicate that major changes to the behavioral evolution occurred during the Late Cretaceous and the Early Eocene. Previous hypotheses about Late Cretaceous evolutionary influences were validated. However there were additional influences like the Paleocene-Eocene Thermal Maximum that were not overly emphasized before. Finally, of the many theories about the driving force of evolution, chaos theory has often been overlooked. Chaos theory is a powerful tool, such that, by knowing the similarities between chaos theory and evolutionary theory, it may be possible to map out how environmental changes could shift the evolution of a species

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described