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Onsager Differential Equation

The ordinary Onsager equation is the sixth-order ordinary differential equation

(d^3)/(dx^3)[e^x(d^2)/(dx^2)(e^x(dy)/(dx))]=f(x)

(Vicelli 1983; Zwillinger 1997, p. 128), while the partial Onsager equation is given by the partial differential equation

(e^x(e^xu_(xx))_(xx))_(xx)+B^2u_(yy)=F(x,y)

(Wood and Martin 1980; Zwillinger 1997, p. 129).

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References

Vicelli, J. A. "Exponential Difference Operator Approximation for the Sixth Order Onsager Equation." J. Comput. Phys. 50, pp. 162-170, 1983.Wood, H. G. and Morton, J. B. "Onsager's Pancake Approximation for the Fluid Dynamics of a Gas Centrifuge." J. Fluid Mech. 101, 1-31, 1980.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 128-129, 1997.

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Onsager Differential Equation

Cite this as:

Weisstein, Eric W. "Onsager Differential Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OnsagerDifferentialEquation.html

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