Graphical Method for Solving Non-linear Vibrations (E-function method), (Part II)

Modified homotopy perturbation method for solving non-linear oscillator's ‎equations

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...

A METHOD FOR SOLVING FUZZY LINEAR SYSTEMS

In this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. Also necessary and sufficient conditions for existenceof solution are given. Some numerical examples illustrate the efficiencyof the method.

Defuzzification method for solving fuzzy linear systems

T. L. Hill's Graphical Method for Solving Linear Equations

That tree enumeration can be used for solving systems of linear equations was independently realized by physicists [9], electrical engineers [11], chemists [7] and most recently by biophysicists [4, 5]. Going in the opposite direction, mathematicians realized that one can use linear algebra to count trees ([1, p. 378; 8, p. 578; 10, pp. 39-51]). However, both mathematicians and scientists had t...

A non-iterative method for solving non-linear equations

In this paper, using a hyperbolic tangent function tanhðbxÞ, b > 0, we develop a non-iterative method to estimate a root of an equation f(x) = 0. The problem of finding root is transformed to evaluating an integral, and thus we need not take account of choosing initial guess. The larger the value of b, the better the approximation to the root. Alternatively we employ the signum function sgnðxÞ ...