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In this paper, we use homotopy method to transfer nonlinear equations to a differential equations, then we apply four-order Runge-Kutta method to solve the differential equations for getting a more stable and easily convergent solution. What is more important, we demonstrate a complete proof of the whole process, which provide a scientific foundation for the method as a whole. In the end, we give...
In this paper, nonlinear three-point boundary value problems for a class of third order nonlinear differential equations is studied by means of differential inequality theories and upper and lower solutions. Based on the given results of second order boundary value problem, and under suit upper and lower solution, iteration sequences were constructed, and existence and unique of solutions of nonlinear...
This paper discussed numerical algorithm of the initial and boundary value problem of nonlinear ordinary differential equations and analysis its stability in computer. The iterated algorithm with spline function for initial value problem in nonlinear ordinary differential equations was studied. Based on the principle of Newton's algorithm for nonlinear equation, a parallel algorithm for initial value...
In this paper, a new family of combined iterative methods for the solution of nonlinear equations is presented.The new family of methods is based on Newton's method and the family of sixth-order iterative methods developed by Chun. Per iteration the new methods require three evaluations of the function and two evaluations of its first derivative. Numerical tests show that it takes less number of iterations...
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