Mathematica Help with nonlinear differential?

In summary, the conversation discusses a problem with using DSolve to solve a function involving h[t] and h[0]. The solution involves replacing h[0] with a constant and then finding the value of h[0] that maximizes another function. There is a concern about whether this approach will work if h[0] is not originally included in the h[t] function. Links to the relevant notebook and PDF are also provided.
  • #1
sirion
Having some troubles getting further in this system I'm trying to solve. The notebook's at http://www.gabrielwyner.com/fluids5.nb

PDF form:
http://www.gabrielwyner.com/fluids5.pdf

I guess the most current problem involves mathematica complaining about DSolve[h'[t] = f[h[t],h[0]]] (with correct syntax, that is). It doesn't like solving a function with h[t] and h[0] in it..
 
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  • #2
Try replacing h[0] with some arbitrary constant, k... then (at some point) imposing the initial condition that h[0] = k.
 
  • #3
That works, but eventually I need to solve for the h[0] that maximizes another function of h[t]. Was hoping to get a function for h[t], plug it into u[t], plug that into v[t], plug *that* into k[t] and plot that vs h[0]. Am I going to run into trouble if h[0] isn't part of the original h[t] function?
 

What is Mathematica?

Mathematica is a software program used for mathematical, scientific, and engineering calculations. It is designed to handle complex computations and provide solutions to equations and problems.

What is a nonlinear differential equation?

A nonlinear differential equation is an equation that involves derivatives of a function with respect to one or more independent variables, and the function itself appears in a nonlinear form. This means that the rate of change of the function is not directly proportional to the function itself.

How can Mathematica help with solving nonlinear differential equations?

Mathematica has built-in functions and algorithms specifically designed to solve nonlinear differential equations. These functions can accurately and efficiently find solutions to a wide range of nonlinear differential equations.

Can Mathematica handle systems of nonlinear differential equations?

Yes, Mathematica is capable of solving systems of nonlinear differential equations. It has powerful tools for solving coupled differential equations and can handle systems with multiple variables and initial conditions.

Do I need to have advanced knowledge of Mathematica to use it for solving nonlinear differential equations?

While having some familiarity with Mathematica can be helpful, it is not necessary to have advanced knowledge of the software to use it for solving nonlinear differential equations. The built-in functions and step-by-step tutorials make it user-friendly for beginners as well.

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