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Recent Modifications of Adomian Decomposition Method for Initial Value Problem in Ordinary Differential Equations
Adomian Decomposition Method Initial Value Problem Modified Adomian Decomposition Method
2013/1/30
In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are appl...
Semipositone Problems of Second Order Ordinary Differential Equations
Positive solution Semipositone boundary value problem Ordinary differential equation
2011/10/12
The paper is concerned with the semipositone boundary value problems of second-order ordinary differential equations. Applying a fixed point theorem in cones, an existence result of at least one posit...
Analytic solutions of parametric type and numerical simulations of a class of nonlinear ordinary differential equations
BVP analytic solutions of parametric type
2010/9/25
In this paper, the mathematical model that describes the radially symmetric deformation of a micro-void centered at a compressible hyperelastic sphere is formulated as a boundary value problem (BVP) o...
Unnecessary Exact Solutions of Nonlinear Ordinary Differential Equations
Unnecessary Exact Solutions Nonlinear Ordinary Differential Equations
2010/11/10
We analyze the paper by Wazwaz and Mehanna [Wazwaz A.M., Mehanna M.S., A variety of exact travelling wave solutions for the (2+1) -- dimensional Boiti -- Leon -- Pempinelli equation, Appl. Math. Comp....
Positive periodic solutions of singular systems of first order ordinary differential equations
Periodic solutions singular system Krasnoselskii fixed point
2010/12/10
The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions atinfinity for an appropriately ...
A numeric-analytical method for solving the Cauchy problem for ordinary differential equations
FD-method Adomian decomposition method generating function method ordinary di erential equation Cauchy problem
2010/11/26
In the paper we o er a functional-discrete method for solving the Cauchy problem for the rst order ordinary di erential equations (ODEs). This method (FD-method) is in some sense similar to the Adomi...
Periodic boundary value problem for second order ordinary differential equations
Boundary value problems periodic solution
2010/9/10
In this paper we study the periodic boundary value problem for a nonlinear ordinary differential equation of second order. We give sufficient and necessary conditions for the existence of periodic sol...
Rearrangements of the Coefficients of Ordinary Differential Equations
Rearrangements Nonconvex set Extremal couples
2008/6/27
We establish extremal values of a solution y of a second-order initial value problem as the coefficients vary in a nonconvex set. These results extend earlier work by M. Essen in particular by allowin...
In this paper, we develop a new teclinique called multiplicative extrapolation method which is used to construct higher order schemes for ordinary dtherential equations. We call it a new method becaus...
Rational General Solutions of Algebraic Ordinary Differential Equations
Rational general solution algebraic di® erential equation autonomous ˉrst order ODE algebraic curve rational parametrization Pad¶ e approximants
2013/9/9
We give a necessary and su±cient condition for an algebraic ODE to have a rational type general solution. For an autonomous ˉrst order ODE, we give an algorithm to compute a rational general solution ...
Transformations of ordinary differential equations via Darboux transformation technique
ordinary differential equations Darboux transformation technique
2010/11/1
A new approach for obtaining the transformations of solutions of nonlinear ordinary differential equations representable as the compatibility condition of the overdetermined linear systems is propose...