Non-polynomial Fourth Order Equations which Pass the Painlevé Test

Non-polynomial Fourth Order Equations which Pass the Painlevé Test

Painlevé and his school [1 – 3] studied the certain class of second order ordinary differential equations (ODEs) and found fifty canonical equations whose solutions have no movable critical points. This property is known as the Painlevé property. Distinguished among these fifty equations are six Painlevé equations, PI – PVI. The six Painlevé transcendents are regarded as nonlinear special funct...

Non-polynomial third order equations which pass the Painlevé test

The singular point analysis of third-order ordinary differential equations in the nonpolynomial class are presented. Some new third order ordinary differential equations which pass the Painlevé test as well as the known ones are found.

NON-POLYNOMIAL SPLINE SOLUTIONS FOR SPECIAL NONLINEAR FOURTH-ORDER BOUNDARY VALUE PROBLEMS

We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications ...

Fourth Order Equations In

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence