For Initial Value problems I want to implement an ODE solver for implicit Euler method with adaptive time step and use step doubling to estimate error. I have found some reading stuff about adaptive time step and error estimation using step doubling but those are mostly related to RK methods. I...
The question is very general and could belong to another topic, but here it is.
Suppose one wants to solve the set of differential equations $$ \frac{\partial x}{\partial t}=\frac{\partial H(x,p)}{\partial p},$$ $$\frac{\partial p}{\partial t}=-\frac{\partial H(x,p)}{\partial x},$$ with some...
1. Homework Statement
a. Given u=F(x,y,z) and z=f(x,y) find { f }_{ xx } in terms of the partial derivatives of of F.
b. Given { z }^{ 3 }+xyz=8 find { f }_{ x }(0,1)\quad { f }_{ y }(0,1)\quad { f }_{ xx }(0,1)
2. Homework Equations
Implicit function theorem, chain rule diagrams, Clairaut's...
Good Day
Let's say I have developed a new method to extract, more efficiently (yes, "more efficiently" is ill-defined; but bear with me) the differential equations that describe a specific phenomena (please just assume it).
So now I have a system of coupled second order differential...
Is there any research that was done on animal long and short term memories?
And short of empirical analysis, if there is none, is there much we could conclude, based purely on what we know about their brains?
For example, from knowing which brain parts deal with explicit and which with...
Im trying to implement the implicit Euler method in high-performance software for micromagnetic simulations, where I'm restricted to using the driving function of the ODE (Landau-Lifshitz equation) and the previous solution points. This obviously not a problem for an explicit method, since we...
1. Homework Statement
with answers given:
2. Homework Equations
use implicit differentiation
3. The Attempt at a Solution
I always get this answer
but not the second one
PLs explain the second answer for I am very desperate.
Thank You