Hope I have posted this in the right section, this question is half differential equation and half finite difference method. The equation I have is a form of the Lucas Washburn equation, which is concerned with capillary rise:

[tex]\rho\left[\left(z+\lambda\right)z''_{tt}+(z'_{t})^{2}\right]+Vzz'_{t}+\rho g z=F[/tex]

[tex]\lambda,\rho[/tex], F & V are constants,initial conditions are z(0)=0, and z'(0)=0

The Equation in another form:

[tex]z\ddot{z}+\dot{z}^{2}=az\dot{z}+bz+c[/tex]

Am I correct in thinking that this differential equation has no analytical solution? In light of that I want to try and solve for z(t) numerically using a finite difference method but am unsure about how to reform this equation into a from I can use. Any thoughts or suggestions would be greatly appreciated.

Teller

[tex]\rho\left[\left(z+\lambda\right)z''_{tt}+(z'_{t})^{2}\right]+Vzz'_{t}+\rho g z=F[/tex]

[tex]\lambda,\rho[/tex], F & V are constants,initial conditions are z(0)=0, and z'(0)=0

The Equation in another form:

[tex]z\ddot{z}+\dot{z}^{2}=az\dot{z}+bz+c[/tex]

Am I correct in thinking that this differential equation has no analytical solution? In light of that I want to try and solve for z(t) numerically using a finite difference method but am unsure about how to reform this equation into a from I can use. Any thoughts or suggestions would be greatly appreciated.

Teller

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