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Questions tagged [computational-science]

Use this tag for questions about advanced computing to model, simulate, understand, or solve engineering, biological, physical, social, and humanities problems.

Computational science is a multidisciplinary field that uses advanced computing to model, simulate, understand, or solve engineering, biological, physical, social, and humanities problems.

Computational science encompasses the areas of—

  • numerical and non-numerical algorithms,
  • computer and information science (used to develop and optimize advanced system hardware, software, networking, and data management to solve computationally demanding problems), and
  • computing infrastructure.

Computational science is to be contrasted with laboratory experiment and theory, the traditional methods of science and engineering. With computational science, scientists and engineers develop computer programs that model systems being studied and run those programs with various sets of input parameters. In some cases, those models require massive amounts of calculations and are often executed on supercomputers or distributed computing platforms.

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Why do the following two Partial Differential Equations have the same continuous solutions but different discontinuous solutions?

I am considering the following two problems: $$ u_t + \left( \frac{u^2}{2} \right)_x = 0 $$ and $$ \left( \frac{u^2}{2} \right)_t + \left( \frac{u^3}{3} \right)_x = 0 $$ I know that these Equations have the same continuous solutions. I am now…
Math Undergrad Student
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What is the partial differential symbol (bent lowercase $d$) with an $x$ at the top?

From a government website on global warming: $PT = LT / (1 - s)$, where the sensitivity coefficient $s = ðln(LT) / ðln(B)$ and $B =$ burden. I have seen this before, yet there is never an explanation as to what it means.....
Kurt Hikes
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Achievable speedup of matrix-vector products with sparse matrix storing formats

I have recently done a rather extensive numerical study of the effect of sparse matrix storing formats on the runtime of matrix-vector products. In particular, I considered the following formats: CSR, CSC, COO, BCSR and MBR (See Kannan, 2013 for a…
Nicolas Venkovic
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Is the entire field of "membrane computing" vaporware?

I came across this concept of membrane computing, which appears to have been created entirely by a mathematician from my country (Romania), and further developed by his son, also a mathematician. At a glance, it seems to be a very prolific field,…
Axl Vang
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Setting up Very Simple PDE Resembling Ice Flow Full Stokes for a Toy FEM Problem

My main goal is to come up with a very very simple model that resembles a simple version of the Full Stokes equations used in ice flow modeling. I would like to take the viscosity to be constant in my model. I entirely understand that the viscosity…
k12345
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How to solve the equation $\sqrt{\frac{\sqrt{x!}\times \sqrt{x!!}\times \sqrt{x!!!}}{\sqrt{\left( x-2 \right)!+x}}}=12$

Consider the following equation, $$\sqrt{\frac{\sqrt{x!}\times \sqrt{x!!}\times \sqrt{x!!!}}{\sqrt{\left( x-2 \right)!+x}}}=12$$ I tried first to eliminates all radicals using squring both sides to get the following , $$\frac{\sqrt{x!}\times…
Ramez Hindi
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Error bound for nonlinear finite difference approximations

Let's say we have a second-order central difference approximation for the first derivative: $$\frac{\partial f(x_j)}{\partial x} = \frac{f(x_j + h)-f(x_j - h)}{2h} + O(h^2)$$ Is it true that: $$\left(\frac{\partial f(x_j)}{\partial x}\right)^2 =…
S. Green
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Why does standard finite elements method fails with transient problems?

Consider the one-dimensional wave equation $u_{tt} - c^2 u_{xx} = 0$ defined on a finite domain. I have tried to simulate the propagation of a discontinuous wave by using FEM with piecewise-linear shape functions and time-stepping techniques such…
cgyo
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How are floating-point numbers logarithmically distributed?

From what I remember from a lecture I had of a course I'm attending called "introduction to computational science", floating-point numbers are distributed logarithmically. What does it mean? And how can I visualize it? I've a slide where it is…
user168764
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Algebraic Grid Generation

I am new to topic " Algebraic Grid Generation". I want to find a simple example where we solve the host equation, let us say the heat equation, numerically in the computational domain then transform it back to the physical domain. All the references…
Mahmoud Saleh
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How to show that the following series converges to the correct answer:

I am studying computational physics using 'Computational Physics Problem Solving with Python, 3rd edition' by Rubin H. Landau and others and it contains a problem for finding approximate value of sin(x) using the series summation…
Pranjal
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What are the most known and optimized libraries for SDE in Python?

I am using Python for solving a large size system of stochastic differential equations (SDE) of the form $\rm{d}\textbf{x}=A\textbf{x}\rm{d}t+b\rm{d}W$, where A and b are a matrix and vector respectively of suitable size and $\rm{d}W$ represents a…
Camilo160
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Runge Kutta adaptive step size collapses to 0

I am trying to solve numerically a problem in orbital motion, using Runge-Kutta 4 method with adaptive step size. Because energy is the most obvious theoretically conservative number in the motion, I want to dymically control the step size of the…
Frogfire
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How does one find all the fixed points of the Hodgkin-Huxley Model?

I'm trying to find the fixed points of the Hodgkin-Huxley model, given by the system of…
Andopolous
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basic level maths to geometrical interpolations (trilinear, prism, pyramid, tetrahedral) - where do I start?

I'm attempting to read Computational Color Technology by Henry R. Kang but I only have a GCSE level understanding of maths (if even that, it was 15 years ago..). I'd like to learn about geometrical interpolations (trilinear, prism, pyramid,…
Harry Bennett-Snewin
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