The Approximate Solution of Linear Differential Equations

1948 ◽  
Vol 27 (2) ◽  
pp. 350-364 ◽  
Author(s):  
Marion C. Gray ◽  
S. A. Schelkunoff
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
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.

Straightening expansions of gas from vortex with linear velocity field

2012 ◽  
Vol 9 (2) ◽  
pp. 143-148
Author(s):  
Yu.V. Yulmukhametova
Keyword(s):  
Approximate Solution ◽  
Velocity Field ◽  
Initial Data ◽  
Differential Equations ◽  
First Integrals ◽  
Linear Differential Equations ◽  
The World ◽  
Linear Velocity Field ◽  
Linear Differential ◽  
Linear Field

In work one submodel of flow of gas with the linear field of speeds is considered. It is formed by system of non-linear differential equations with initial data. Several first integrals of such system are found. For express initial data of a task approximate solution of differential equations of a submodel is found. To such decision there correspond the world lines describing the becoming straight scattering of particles of gas from a whirlwind. Trajectories of driving of particles of gas are constructed.

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