# All Questions

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### What's the simplest way to graph a 2d array generated in C++ using Windows 7?

This was so much easier in Python (so much so that I'm considering going back to matplotlib for data analysis). But really, trying to figure out ROOT and Boost graph library and mathgl makes me want ...
70 views

### Pros of Fourier-Galerkin spectral methods

What are the pros of Fourier-Galerkin spectral methods while solving PDEs? Here's the one that came in my mind first: Easy implementation: using this method, differentiation operator computation is ...
63 views

### How is the final result calculated in RK-Dopri(4,5)?

I have found a toy implementation of RK-Dopri(4,5), written in Python. I am concerned however, about line 118: y = y + h * (b1*K1+b3*K3+b4*K4+b5*K5+b6*K6) Has the ...
37 views

### Maximum lossless compression ratio for floating point time series

I want to compress an array of time series floating point data as much as possible. Currently the only algorithm I've found for this is XOR compression which works well, but doesn't compress the data ...
60 views

### Reading VTK file into C++ for analysis

I apologize in advance if this post is at all ignorant or elementary, I am a pure mathematician who is newly getting into the world of scientific computing. For my research, my advisor would like me ...
271 views

### Is there a minimum angle requirement for cells in the finite volume method?

In his talk "What is a good linear finite element?", Shewchuk states that small dihedral angles in linear tetrahedra elements cause ill-conditioning of the stiffness matrix. Do small dihedral angles ...
44 views

116 views

### Numerically finding constants of motion

Given a set of ODE's $\dot{z} = f(z)$ (or discrete time $z_{t+1} = f(z_t)$), is there a way to numerically find constants of motion? For $f(z_t) \approx M z_t$, diagonalizing the matrix $M$ ...
445 views

395 views

### Is there a database/website with Butcher tableaus?

I have started investigating in mostly Runge Kutta and Runge Kutta Nyström methods and there one of the only differences between the methods of the same type is their Butcher tableu. For the most ...
196 views

### Method to solve linear, first order ODE of generalized matrix matrix form

The equation and its meaning: Consider two sets $(A)_{l=0,...,m_a},$,$(B)_{l=0,...,m_b}$ of hermitian matrices and a set of positive semidefinite matrices $(C)_{l=0,...,m_c}$. Each matrix has the ...
116 views

### Runge-Kutta timestep in atomic units

I'm using 4th order RK to solve the schroedinger equation in atomic units. Say I want to simulate 400fs in intervals of h=10fs, then in atomic units this is h=413a.u and 400fs=16500a.u. 4RK involves ...
302 views

### Runge Kutta and Milstein – system of second-order coupled differential equations with noise

I would like to solve a system of second-order differential equations to describe the dynamics of a system of particles. Two Newton-like forces are responsible for the motion of each particle $i$: A ...
944 views

### How to integrate numerically Nosé Hoover equation?

In NVT molecular dynamics, Nosé Hoover thermostat is a method defining an extended system. I can understand perfectly how the Nosé Hoover differential equations are derived (Frenkel&Smit's book). ...
587 views

### How to implement an integral condition when solving a BVP in MatLab

I am trying to solve a coupled system of ODE's using MATLAB's bvp4c function. I want to impose the condition that $$\int_{0}^{\pi} y_{1}(t) y_{1}(t) dt = 1,$$ where ...
57 views

### Integrating a nonlinear ordinary differential equation

I am solving an equation of the form $(*)$ $0 = a(f) (\partial_rf)^2 + b(f) (\partial_rf) + c(f),$ where $f$ is a real function of $r\in \mathbb{R}$, and $a,b,c$ are real functions of $f$. The ...
126 views

### Recommendation for a fixed-step ODE solver?

My problem involves the solution of a second-order ODE with a fixed-step (input and output). Specifically, this ODE is the radial part of Dirac and Schrödinger equation for a spherical symmetric ...
129 views

### Solving numerically a linear ODE

I start by saying that I do not have a strong background in numerical analysis, so I may miss some basic things or make trivial mistakes. Motivated by some problems in digital signal processing, I ...
136 views

### Lambdifying a symbolic matrix in Julia

If I have a symbolic matrix defined as T below, is there any way to lambdify this as function of variables, say σ..., and return ...
228 views

### How well do explicit Runge-Kutta “tableau” methods compare to the state of the art ODE solvers and when do they fail?

How well do explicit Runge-Kutta "tableau" methods compare to the state of the art ODE solvers and when do they fail? I've been reading Butcher's ODE book and he does a good job at introducing ...
125 views

### Parallel integration of dynamical systems

I need to solve the following problem: $$\begin{cases} \dot{\vec{x(t)}} = A\vec{x(t)} + u(t)D\vec{x(t)} + u(t)\vec{b}, & x \in (0, T), \\ \vec{x(0)} = \vec{0}, \end{cases}$$ where $u(t)$ is known ...
347 views

### Forward and backward integration — cause of errors

I write a test program to integrate foward on $[0,T_f]$ and then backward on $[T_f,0]$ from the endpoint of the forward integration an Hamiltonian system:  \dot q(t) = \frac{\partial H}{\partial p}(...
326 views

### The Formula of Explicit Runge-Kutta Fourteen order

I need an explicit Runge-Kutta 14th order formula. If you know about some reference that discusses at least 10th order (or higher, since I'm looking for the 14th) of Runge-Kutta and there is ...
177 views

### Has anyone used Julia to write a PDE solver?

I've tinkered with Matlab's PDE toolbox for a while but was wondering whether anyone here has used Julia to build a PDE solver. If so, what are the advantages and limitations of Julia for PDEs? I'm ...
266 views

### Recommended language/environment for large scale semi-continuous biological models

We have a fairly large (maybe 1000 equations) differential-algebraic equation model written in ACSLX, an obsolete modelling environment similar to Modelica. The model represents the evolution of a ...