Iterative Method for Solving a Fourth Order Differential Equation with Nonlinear Boundary Condition
نویسندگان
چکیده
In this paper we consider a fourth order differential equation with nonlinear boundary condition. The existence and uniqueness of a solution is proved. An iterative method for its solution is proposed and the convergence of the method is established. An interesting property of the sequence of iterative solution in dependence of the monotonicity of the function in nonlinear BC is investigated. Numerical examples illustrate the convergence and the properties of the sequence of approximate solutions. Mathematics Subject Classification: 65L10, 34B15
منابع مشابه
The smoothed particle hydrodynamics method for solving generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system
A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...
متن کاملIterative method for solving a nonlinear fourth order boundary value problem
In the study of transverse vibrations of a hinged beam there arises a boundary value problem for fourth order ordinary differential equation, where a significant difficulty lies in a nonlinear term under integral sign. In recent years several authors considered finite approximation of the problem and proposed an iterative method for solving the system of nonlinear equations obtained. The essenc...
متن کاملIterative scheme to a coupled system of highly nonlinear fractional order differential equations
In this article, we investigate sufficient conditions for existence of maximal and minimal solutions to a coupled system of highly nonlinear differential equations of fractional order with mixed type boundary conditions. To achieve this goal, we apply monotone iterative technique together with the method of upper and lower solutions. Also an error estimation is given to check the accuracy of th...
متن کاملThe spectral iterative method for Solving Fractional-Order Logistic Equation
In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...
متن کاملOn Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory
In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...
متن کامل