scholarly journals Solvability of systems of ordinary differential equations in the space of Aronszajn and the determinant over the Weyl algebra

1990 ◽  
Vol 117 ◽  
pp. 207-225 ◽  
Author(s):  
Masatake Miyake
Keyword(s):  
Differential Equations ◽  
Heat Equation ◽  
Ordinary Differential Equations ◽  
Weyl Algebra ◽  
Analytic Solutions ◽  
Fréchet Space ◽  
Frechet Space

N. Aronszajn introduced in [4] an abstract Frechét space R (0<R≤∞), which is isomorphic to the space of analytic solutions of the heat equation in if 0 < R ∞, and in if R = ∞, and called it the space of traces of analytic solutions of the heat equation. Hereafter, we call it the space of traces, shortly.

Transversal Method of Lines for Unsteady Heat Conduction With Uniform Surface Heat Flux

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Antonio Campo ◽  
José Garza
Keyword(s):  
Heat Flux ◽  
Differential Equations ◽  
Heat Equation ◽  
Ordinary Differential Equations ◽  
Surface Heat Flux ◽  
Method Of Lines ◽  
Surface Heat ◽  
Second Order ◽  
Partial Differential ◽  
Stationary Heat

The transversal method of lines (TMOL) is a general hybrid technique for determining approximate, semi-analytic solutions of parabolic partial differential equations. When applied to a one-dimensional (1D) parabolic partial differential equation, TMOL engenders a sequence of adjoint second-order ordinary differential equations, where in the space coordinate is the independent variable and the time appears as an embedded parameter. Essentially, the adjoint second-order ordinary differential equations that result are of quasi-stationary nature, and depending on the coordinate system may have constant or variable coefficients. In this work, TMOL is applied to the unsteady 1D heat equation in simple bodies (large plate, long cylinder, and sphere) with temperature-invariant thermophysical properties, constant initial temperature and uniform heat flux at the surface. In engineering applications, the surface heat flux is customarily provided by electrical heating or radiative heating. Using the first adjoint quasi-stationary heat equation for each simple body with one time jump, it is demonstrated that approximate, semi-analytic TMOL temperature solutions with good quality are easily obtainable, regardless of time. As a consequence, usage of the more involved second adjoint quasi-stationary heat equation accounting for two consecutive time jumps come to be unnecessary.

Families of analytic solutions for (2+1) model in unbounded domain via optimal Lie vectors with integrating factors

2019 ◽  
Vol 33 (20) ◽  
pp. 1950229 ◽  
Author(s):  
R. Sadat ◽  
M. M. Kassem ◽  
Wen-Xiu Ma
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Unbounded Domain ◽  
Analytic Solutions ◽  
Symmetry Reduction ◽  
Lie Symmetry ◽  
Two Stages ◽  
Integrating Factors

Through the commutator table and the adjoint table between the infinitesimals, we apply two stages of Lie symmetry reduction to reduce the (2[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation to ordinary differential equations (ODE’s). Some of these ODE’s had no quadrature. We derive several new solutions for these non-solvable ODE’s using Integrating Factors property.

Systems of Briot-Bouquet Equations with Analytic Solutions

1982 ◽  
Vol 25 (2) ◽  
pp. 230-233
Author(s):  
David Westreich ◽  
Ester Podolak
Keyword(s):  
Functional Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Singular System ◽  
Analytic Solutions

AbstractIn this note we use functional analysis arguments to prove the existence of families of analytic solutions for the singular system of complex ordinary differential equations zW′ = h(z, W).

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