Computer Methods in Applied Mechanics and Engineering

https://irafm.osu.cz/research_report/131_rep130.pdf

On fuzzifications of discrete dynamical systems

A new approach to solving fuzzy real and complex systems of linear equations based on the fuzzy center and width is presented here. The unknown variable and right-hand side vector are considered as fuzzy, whereas the coefficient matrix is considered as crisp. First the system is solved in terms of the fuzzy center, and then this solution is used with the width to get the final solution of the original system. The presented procedure is applied to analyze three example problems. The results obtained are also compared with the known solutions and are found to be in good agreement.

A new method for solving real and complex fuzzy systems of linear equations

Numerical solution of nonlinear fuzzy Fredholm integral equations using iterative method

In this paper, systems of linear differential equations with crisp real coefficients and with initial condition described by a vector of fuzzy numbers are studied. A new method based on geometric representations of linear transformations is proposed to find a solution. The most important difference between this method and methods offered in other papers is that the solution is considered to be a fuzzy set of real vectorfunctions rather than a vector of fuzzy functions. Each member of the solution set satisfies the given system with a certain possibility. It is shown that at any time the solution constitutes a fuzzy region in the coordinate space, alpha-cuts of which are nested parallelepipeds. The proposed method is illustrated on examples.

A Geometric Approach to Solve Fuzzy Linear Systems of Differential Equations

Invariant subspaces, exact solutions and stability analysis of nonlinear water wave equations

Predictor-corrector methods for nonlinear fuuzy Volterra integral equations are considered together with a theorem which provides a proof of the convergence of such methods. A numerical example is also included.

Predictor-Corrector Method for Nonlinear Fuzzy Volterra Integral Equations

An effective scheme for solving system of fractional Volterra–Fredholm integro-differential equations based on the Müntz–Legendre wavelets

A note on Fuzzy differential equations and the extension principle

In this paper, we study the m £ n fuzzy linear system (m > n) using a numerical method. A numerical method for finding least-squares solution of an overdetermined fuzzy system of linear equation by applying an orthogonal matrix to coefficients matrix is given. we show here the orthogonal matrix has special structure if the coefficient matrix has too. Procedure for calculating the solution is illustrated in some examples. Copyright © 2008 Yang's Scientific Research Institute, LLC. All rights reserved.

Mahmoud Shafiee

Papers

Invariant subspaces, exact solutions and stability analysis of nonlinear water wave equations

Predictor-Corrector Method for Nonlinear Fuzzy Volterra Integral Equations

An effective scheme for solving system of fractional Volterra–Fredholm integro-differential equations based on the Müntz–Legendre wavelets

A note on Fuzzy differential equations and the extension principle

Revised Solution of an Overdetermined Fuzzy Linear System of Equations