1. T

    A Implicit Euler method with adaptive time step and step doubling

    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...
  2. F

    A Numerical solution of Hamiltonian systems

    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...
  3. S

    Partial derivatives and chain rule

    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...
  4. O

    Selecting a numerical method

    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...
  5. seyfi

    2d heat equation ADI method

    Hi all Do you know how to write code Alternating Direct Implicit(ADI) method in Matlab? I have given 2d heat equation for this. Thank you
  6. I

    Different animal sensory, short and long term memories?

    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...
  7. P

    Matrix-free iteration methods and implicit ODE solvers

    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...
  8. funlord

    Implicit Differentiation: two different answers

    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