Lazarus Fuchs′ Transformation for Solving Rational First-Order Differential Equations

DIFFERENTIAL TRANSFORMATION METHOD FOR SOLVING FUZZY FRACTIONAL HEAT EQUATIONS

In this paper, the differential transformation method (DTM) was applied to solve fuzzy fractional heat equations. The elementary properties of this method were given. The approximate and exact solutions of these equations were calculated in the form of series with easily computable terms. The proposed method was also illustrated by some examples. The results revealed that DTM is a highly effect...

Rational solutions of first-order differential equations∗

We prove that degrees of rational solutions of an algebraic differential equation F (dw/dz,w, z) = 0 are bounded. For given F an upper bound for degrees can be determined explicitly. This implies that one can find all rational solutions by solving algebraic equations. Consider the differential equation F (w′, w, z) = 0, (w′ = dw/dz) (1) where F is a polynomial in three variables. Theorem 1 For ...

A new approach for solving the first-order linear matrix differential equations

Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the first-order linear matrix differential equations. Properties of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solvin...

A method for solving first order fuzzy differential equation

Telescoping Decomposition Method for Solving First Order Nonlinear Differential Equations

The Telescoping Decomposition Method (TDM) is a new iterative method to obtain numerical and analytical solutions for first order nonlinear differential equations. The method is a modified form of the well-known Adomian Decomposition Method (ADM) where the Adomian polynomials have not to be calculating. The (TDM) is easier to apply and offers better accuracy than the (ADM). Also, it can be appl...