An Improved Method of Undetermined Coefficients
نویسنده
چکیده
Abstract: An exact solution method in terms of an infinite power series is developed for linear ordinary differential equations with polynomial coefficients. The method is general and applicable to a wide range of equations of any Nth order presented in normal form. The final solution is defined by a linear combination of S functions fj(x) j=1,...,S expressed in the form of a power series, and by additional (S-N) number of accompanied relationships for unknown constants. Each term of the series fj(x) is defined by a finite number of operations involving matrix calculations. The term calculation is independent on unknown constants.
منابع مشابه
Buckling Analysis of Cantilever Nanoactuators Immersed in an Electrolyte: A Close Form Solution Using Duan-Rach Modified Adomian Decomposition Method
A new modified Adomian Decomposition Method (ADM) was utilized to obtain an analytical solution for the buckling of the nanocantilever actuators immersed in liquid electrolytes. The nanoactuators in electrolytes are subject to different nonlinear forces including ionic concentration, van der Waals, external voltage and electrochemical forces. The Duan–Rach modified Adomian decomposition method ...
متن کاملSome modification of Newton's method by the method of undetermined coefficients
In this paper, we construct some modifications of Newton’s method for solving nonlinear equations, which is based on the method of undetermined coefficients. It is shown by way of illustration that the method of undetermined coefficients is a promising tool for developing new methods, and reveals its wide applicability by obtaining some existingmethods as special cases. Two new sixth-ordermetho...
متن کاملLecture 16 - Second order nonhomogeneous linear differential equations: Method of Undetermined Coefficients
In this lecture we learn to solve nonhomogeneous equations of the form ay′′ + by′ + cy = g(t) using the “method of undetermined coefficients”. In previous lectures we learned to how to solve any equation of the form ay′′ + by′ + cy = 0. We will apply these techniques to help us solve the nonhomogeneous equation ay′′ + by′ + cy = g(t) by understanding the connection between solutions to homogene...
متن کاملAn Improved Correlation for Second Virial Coefficients of Pure Fluids
In the present work, a modified correlation is presented for the second virial coefficients of both polar and nonpolar fluids based on the corresponding states principle. The second virial coefficients of gaseous polar and non-polar compounds were calculated and compared with experimental data and with other correlations. Comparisons with the existing correlations show that the present work is ...
متن کاملAn improved and efficient stenographic scheme based on matrix embedding using BCH syndrome coding.
This paper presents a new stenographic scheme based on matrix embedding using BCH syndrome coding. The proposed method embeds massage into cover by changing some coefficients of cover. In this paper defining a number :::as char:::acteristic of the syndrome, which is invariant with respect to the cyclic shift, we propose a new embedding algorithm base on BCH syndrome coding, without finding ro...
متن کامل