Classroom Note: Numerical solutions of Nagumo's equation

Nagumo's equation is a third order non-linear ordinary differential equation d3udx3−cd2udx2+f′(u)dudx−(b/c)u=0 where f(u)=u(1−u)(u−α) , 0<α<1 . In this paper we have developed a technique to determine those values of the parameters a,b and c which permit non-constant bounded solutions.

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Construction of Green’s functional for a third order ordinary differential equation with general nonlocal conditions and variable principal coefficient

Georgian Mathematical Journal ◽

10.1515/gmj-2019-2003 ◽

2020 ◽

Vol 27 (4) ◽

pp. 593-603 ◽

Cited By ~ 1

Author(s):

Kemal Özen

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Nonlocal Problem ◽

Nonlocal Conditions ◽

Adjoint Problem ◽

Linear Ordinary Differential Equation ◽

Third Order ◽

Order Ordinary Differential Equation ◽

Order Linear ◽

Theoretical Results

AbstractIn this work, the solvability of a generally nonlocal problem is investigated for a third order linear ordinary differential equation with variable principal coefficient. A novel adjoint problem and Green’s functional are constructed for a completely nonhomogeneous problem. Several illustrative applications for the theoretical results are provided.

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Initiation of thermal explosion by intense light: criticality dependence on data and parameters

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000005403 ◽

1987 ◽

Vol 28 (3) ◽

pp. 287-295 ◽

Cited By ~ 1

Author(s):

K. K. Tam

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Parabolic Equation ◽

Steady State Solution ◽

Linear Ordinary Differential Equation ◽

Critical Parameters ◽

Linear Parabolic Equation ◽

Thermal Ignition ◽

Non Linear ◽

Intense Light

AbstractA model for thermal ignition by intense light is studied. The governing non-linear parabolic equation is linearized in a two-step manner with the aid of a non-linear ordinary differential equation which captures the salient features of the non-linear parabolic equation. The critical parameters are computed from the steady-state solution of the ordinary differential equation, which can be obtained without actually solving the equation. Comparison with available data shows that the present method yields good results.

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On the isomonodromic deformation of a linear ordinary differential equation of the third order

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.59.219 ◽

1983 ◽

Vol 59 (6) ◽

pp. 219-222

Author(s):

Hironobu Kimura

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Linear Ordinary Differential Equation ◽

Isomonodromic Deformation ◽

Third Order ◽

The Third

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A System Associated with the Confluent Hypergeometric Function Φ3 and a Certain Linear Ordinary Differential Equation with Two Irregular Singular Points

International Journal of Mathematics ◽

10.1142/s0129167x97000366 ◽

1997 ◽

Vol 08 (05) ◽

pp. 689-702 ◽

Cited By ~ 1

Author(s):

Shun Shimomura

Keyword(s):

Differential Equation ◽

Ordinary Differential Equation ◽

Hypergeometric Function ◽

Confluent Hypergeometric Function ◽

Linear Ordinary Differential Equation ◽

Singular Points ◽

Third Order ◽

Regular Type ◽

Singular Loci ◽

Irregular Singular Points

The confluent hypergeometric function Φ3 satisfies a system of partial differential equations on P1(C) × P1(C) with the singular loci x = 0, x = ∞, y = ∞ of irregular type and y = 0 of regular type. We obtain asymptotic expansions and Stokes multipliers of linearly independent solutions near the singular loci x = 0 and x = ∞. Applying the results we also clarify the global behaviour of the solutions of a third order linear ordinary differential equation with two irregular singular points.

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