Exceptionality Condition and Linearization Procedure for a Third Order Nonlinear PDE

Exact Linearization and Discretization of Nonlinear Systems Satisfying a Lagrange Pde Condition

A sufficient condition for exact linearization of a nonlinear system via an exponential transformation is obtained as a Lagrange partial differential equation. When its solution can be found, the transformation is determined such that the nonlinear systemis exactly converted into a linear system with arbitrary dynamics. When the transformation is invertible, this technique can be applied to exa...

A nonexistence result for a nonlinear PDE with Robin condition

Under the assumption λ > 0 and f verifying f (x, y,0)= 0 in D, 2F(x, y,u)−u f (x, y,u)≥ 0, u = 0, and ifΩ= R×D, we show the convexity of function E(t)= ∫∫D |u(t,x, y)|2dxdy, where u :Ω→R is a solution of problem λ(∂2u/∂t2)−(∂/∂x)(p(x, y)(∂u/∂x))−(∂/∂y)(q(x, y)(∂u/∂y)) + f (x, y,u)= 0 in Ω, u+ ε(∂u/∂n)= 0 on ∂Ω, considered in H2(Ω)∩L∞(Ω), p,q :D→R are two nonnull functions on D, ε is a positive ...

A Third Order Iterative Method for Finding Zeros of Nonlinear Equations

‎In this paper‎, ‎we present a new modification of Newton's method‎ ‎for finding a simple root of a nonlinear equation‎. ‎It has been‎ ‎proved that the new method converges cubically‎.

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS