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Reading: You should have read the entire chapter on Numerical Methods except for the section on numerical methods for partial differential equations, i.e., read 12.1 - 12.5.

Exercises: 12.8, 12.11, 12.12 and 12.14.

Professor,

On Problem 12.11, for a time step of 1, both my 4th order Runge Kutta and 2nd order Runge Kutta are equal to the exact solution at t=3. Is this ok? I wasn't sure because the program asks us to compare the error of different time steps.

Thanks

sschwane wrote:Professor,

On Problem 12.11, for a time step of 1, both my 4th order Runge Kutta and 2nd order Runge Kutta are equal to the exact solution at t=3. Is this ok? I wasn't sure because the program asks us to compare the error of different time steps.

Thanks

The point of the problem is that whenever we derived any equation for numerical methods, it was based on f(x(t),t). For specific f(x,t) it may be the case that all methods seem to have the same order. Explain what you are seeing in this problem, and much, much, much more importantly, why you are seeing it.