Approximate solution of random ordinary differential equations

This is a largely expository paper on approximate methods of solving random ordinary differential equations, with an emphasis on direct numerical methods. Two methods are discussed in some detail and several others are mentioned briefly.

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Approximate solution of random ordinary differential equations

Advances in Applied Probability ◽

10.1017/s0001867800029530 ◽

1978 ◽

Vol 10 (01) ◽

pp. 172-184 ◽

Cited By ~ 1

Author(s):

William E. Boyce

Keyword(s):

Approximate Solution ◽

Numerical Methods ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Approximate Methods ◽

Expository Paper

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The formation of an aerosol by condensation of a dilute vapour in a carrier gas

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1952.0050 ◽

1952 ◽

Vol 211 (1106) ◽

pp. 417-430 ◽

Cited By ~ 4

Keyword(s):

Particle Size ◽

Approximate Solution ◽

Partial Differential Equations ◽

Numerical Methods ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Average Particle Size ◽

Average Particle ◽

Carrier Gas ◽

Rate Of Cooling

The formation of a dilute aerosol by supercooling a mixture of vapour and carrier gas is examined theoretically. It is shown how the partial differential equations of this kind of problem can be reduced approximately to a set of ordinary differential equations, much more easily handled by numerical methods. An approximate solution is obtained which shows how the average particle size depends on the rate of cooling and the time of quenching.

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Numerical Methods for the Eigenvalue Determination of Second-Order Ordinary Differential Equations and Their Applications to Quantum Mechanics

Journal of Computer Chemistry Japan ◽

10.2477/jccj.6.199 ◽

2007 ◽

Vol 6 (3) ◽

pp. 199-216 ◽

Cited By ~ 1

Author(s):

Hideaki ISHIKAWA

Keyword(s):

Quantum Mechanics ◽

Numerical Methods ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Second Order

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Numerical methods for differential algebraic equations

Acta Numerica ◽

10.1017/s0962492900002269 ◽

1992 ◽

Vol 1 ◽

pp. 141-198 ◽

Cited By ~ 67

Author(s):

Roswitha März

Keyword(s):

Numerical Methods ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Differential Algebraic Equations ◽

Algebraic Equations ◽

Image Position

Differential algebraic equations (DAE) are special implicit ordinary differential equations (ODE)where the partial Jacobian f′y(y, x, t) is singular for all values of its arguments.

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