Approximate solution of eigenvalue problems for high-order linear differential equations

1980 ◽  
Vol 20 (4) ◽  
pp. 116-133
Author(s):  
L. Aleksandrov ◽  
D. Karadzhov
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Eigenvalue Problems ◽  
High Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential

The Approximate Calculation of Eigenvalues for Certain Second-Order Linear Differential Equations

1961 ◽  
Vol 65 (605) ◽  
pp. 360-360 ◽  
Author(s):  
W. J. Goodey
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Simple Formula ◽  
Approximate Calculation ◽  
Technical Note ◽  
Second Order ◽  
Numerical Results ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential

In a recent technical note, Squire discussed the approximate solution of certain second-order linear differential equations by the method attributed variously to Riccati, Madelung, Wentzel, Kramers and Brillouin (the W.K.B. method), and others. The problem of eigenvalues, frequently met with in this type of equation, does not, however, appear to have received much attention by this method, and in this note a simple formula is developed which appears to give excellent numerical results in many cases.

scholarly journals Обобщенная задача Римана о распаде разрыва с дополнительными условиями на границе и ее применение для построения вычислительных алгоритмов

2019 ◽  
Vol 170 ◽  
pp. 38-50
Author(s):  
Юрий Иванович Скалько ◽  
Yu I Skalko ◽  
Сергей Юрьевич Гриднев ◽  
S Yu Gridnev
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Hyperbolic System ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linear Differential Equations ◽  
Algebraic Equations ◽  
Order Linear ◽  
First Order ◽  
Linear Differential

We construct an approximation of the fundamental solution of a problem for a hyperbolic system of first-order linear differential equations with constant coefficients. We propose an algorithm for an approximate solution of the generalized Riemann problem on the breakup of a discontinuity under additional conditions at the boundaries, which allows one to reduce the problem of finding the values of variables on both sides of the discontinuity surface of the initial data to the solution of a system of algebraic equations. We construct a computational algorithm for an approximate solution of the initial-boundary-value problem for a hyperbolic system of first-order linear differential equations. The algorithm is implemented for a system of equations of elastic dynamics; it is used for solving some applied problems associated with oil production.

scholarly journals APL and the numerical solution of high‐order linear differential equations

1983 ◽  
Vol 51 (8) ◽  
pp. 743-746
Author(s):  
Neil A. Gershenfeld ◽  
Edward H. Schadler ◽  
O. M. Bilaniuk
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
High Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential

scholarly journals Lucas Polynomial Approach for System of High-Order Linear Differential Equations and Residual Error Estimation

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Muhammed Çetin ◽  
Mehmet Sezer ◽  
Coşkun Güler
Keyword(s):  
Differential Equations ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
High Order ◽  
Linear Differential Equations ◽  
Algebraic Equations ◽  
Order Linear ◽  
Lucas Polynomials ◽  
Linear Algebraic Equations ◽  
Linear Differential

An approximation method based on Lucas polynomials is presented for the solution of the system of high-order linear differential equations with variable coefficients under the mixed conditions. This method transforms the system of ordinary differential equations (ODEs) to the linear algebraic equations system by expanding the approximate solutions in terms of the Lucas polynomials with unknown coefficients and by using the matrix operations and collocation points. In addition, the error analysis based on residual function is developed for present method. To demonstrate the efficiency and accuracy of the method, numerical examples are given with the help of computer programmes written inMapleandMatlab.

Oscillation and Comparison Theorems for Second Order Linear Differential Equations with Integrable Coefficients

1974 ◽  
Vol 26 (02) ◽  
pp. 294-301
Author(s):  
G. Butler ◽  
J. W. Macki
Keyword(s):  
Differential Equations ◽  
Eigenvalue Problems ◽  
Second Order ◽  
Linear Differential Equations ◽  
Comparison Theorems ◽  
Standard Theory ◽  
General Hypothesis ◽  
Order Linear ◽  
Linear Differential ◽  
Image Position

The classical comparison and interlacing theorems of Sturm were originally proved for the equations under the assumption that all coefficients are real-valued, continuous, and p > 0, P > 0. Atkinson [1, Chapter 8] has carried out the standard theory for eigenvalue problems involving (1), under the more general hypothesis

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