Top new questions this week:
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My colleague and I are trying to study the three-body problem, with different integration schemes, starting from the two-body problem. We implemented the symplectic Euler scheme and the Runge–Kutta …
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I’ve noticed that a fairly significant number of cycles in one of my programs are being consumed by the logistic function: $$f(x)=\frac{1}{1+e^{-x}}$$ Is there a good approximation I can use to reduce …
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I am trying to numerically solve a differential equation but I am having trouble getting the convergence test to run properly. The problem is as follows: Consider an ODE $$y'(t) \enspace = \enspace f(…
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I am currently working on writing a MATLAB code for running a finite element simulation of a hyperelastic material in 2D. Since I am building this simulation as a part of a fluid-structure interaction …
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When using the backward and forward Euler methods to solve a certain stiff differential equation, what criteria does one look at before drawing the conclusion that one is more stable than the other?
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I would like to collect some test-problems for nonlinear hyperbolic PDEs (Euler Equations, Shallow Water Equations, Ideal MHD, Acoustic Perturbation, …) for which analytical solutions are known. A …
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I am going to solve this advection equation regarding the flow simulation of an energy tower \begin{equation} Y_t+ v(t) Y_x =0 \end{equation} with the following boundary conditions which depend on …
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Greatest hits from previous weeks:
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So I’ve got a decent head for what problems I work with are best one in serial, and which can be managed in parallel. But right now, I don’t have much of an idea of what’s best handled by CPU-based …
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I’m new to computational science and I already have learned basic methods for integration, interpolation, methods like RK4, Numerov etc on c++ but recently my professor asked me to learn how to use …
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In FEM classes, it’s usually taken for granted that the stiffness matrix is positive definite, but I just can’t understand why. Could anyone give some explanation? For instance, we can consider the …
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I have a system of coupled differential equations, one of which is second-order. I am looking for a way to solve them in Python. I would be extremely grateful for any advice on how can I do that! $k$…
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I’m looking at using OpenFOAM for solving basic internal flows in CFD. What is the best way to get started, and could anyone please point me to a good online reference to go to with any questions I …
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I’m looking into moving some computations of mine to a data center to get more computation power. In the context of this process, I am getting confused by the differentiation of a computation node and …
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I am getting the warning in the post subject when attempting to optimize a function in Python with the scipy.optimize.fmin_bfgs function. The complete output: Warning: Desired error not necessarily …
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