Mixed Nonlinear Conditions Research Articles

Numerical solution of the first order nonlinear differen-tial equations with the mixed nonlinear conditions by using PLSM(comparison with Bernstein polynomials method)

We use the Polynomial Least Squares Method (PLSM), which allows us to compute analytical approximate polynomial solutions for nonlinear ordinary differential equations with the mixed nonlinear conditions. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using Bernstein polynomials method.

Legendre collocation method for solving a class of the second order nonlinear differential equations with the mixed non-linear conditions

Legendre collocation method for solving a class of the second order nonlinear differential equations with the mixed non-linear conditions

Bernstein Collocation Method for Solving the First Order Nonlinear Differential Equations with the Mixed Non-Linear Conditions

In this study, we present the Bernstein matrix method to solve the first order nonlinear ordinary differential equations with the mixed non-linear conditions. By using this method, we obtain the approximate solutions in form of the Bernstein polynomials [1,2,16,17]. The method reduces the problem to a system of the nonlinear algebraic equations by means of the required matrix relations of the solutions form. By solving this system, the approximate solution is obtained. Finally, the method will be illustrated on the examples.

Existence of solutions for fractional q-difference equation with mixed nonlinear boundary conditions

Abstract In this paper, we study the boundary value problem for a class of nonlinear fractional q-difference equation with mixed nonlinear conditions involving the fractional q-derivative of Riemann-Liouuville type. By means of the Guo-Krasnosel’skii fixed point theorem on cones, some results concerning the existence of solutions are obtained. Finally, examples are presented to illustrate our main results. MSC:39A13, 34B18, 34A08.