Special multistep methods based on numerical differentiation for solving the initial value problem

A Comparative Study on the Solutions of 4th Order Differential Equations With Boundary Conditions

“…Stiffly stable methods of higher order have been discussed by Jain [5]. Special multistep techniques using numerical differentiation to solve the IVPs have been discussed by Rao [9]. In particular, the approaches mentioned in this article are focused on the assumption that the solution is better estimated by polynomials.…”

“…In particular, the approaches mentioned in this article are focused on the assumption that the solution is better estimated by polynomials. The inspiration behind the present article is that of Henrici [4], and Rao [9]. Special multistep techniques were derived by substituting y(x) by interpolating polynomial and four times differentiating it.…”

Study of Stability Analysis for a Class of Fourth Order Boundary Value Problems

“…Further information can be had from [7] and [8]. Special multistep methods based on numerical differentiation for solving the initial value problem have been derived in Rama Chandra Rao [9]. The methods now to be discussed are based on replacing the function ( ) ( ) , f x y x which is unknown, by an interpolating polynomial having the values ( )…”

“…The methods discussed in this paper are essentially based on the idea that the solution is best approximated by polynomials. The motivation for the work carried out in this paper arises from the methods based on numerical differentiation for the first-order differential equations, special multistep methods based on numerical integration for the solution of the special second-order differential equations by Henrici [5] and Special multistep methods based on numerical differentiation for solving the initial value problem by Rama Chandra Rao [9]. In Henrici [5] …”

A Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions

“…The essential feature of his analysis is that it leads to the solution of a set of linear equations whose matrix coefficients are of upper Heisenberg form. Bickley uses a special notation other than the conventional one for the representation of the cubic spline, for a detailed discussion one may refer to E. A. Boquez and J. D. A. Walker [2], M. M. Chawla [3], and P. S. Ramachandra Rao [4][5][6][7]. We used Bickley's method for the construction of a sixth degree spline and apply it to the linear fifth order differential equation with two different problems with different boundary conditions.…”