Questions tagged [numerical-integration]

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Slope limiting with implicit time integration

I am solving the advection problem with high order numerical methods, using the method of lines. The boundary conditions and initial condition are selected in a way where I know that the exact ...
vainia's user avatar
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2 votes
2 answers
995 views

Understanding leapfrog integration algorithm

The leapfrog.cpp is an implementation of leapfrog integration algorithm where f() function is being integrated: leapfrog.cpp <...
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1 answer
115 views

How to numerically solve differential equations involving sines, cosines and inverses of the unknown function?

I'm very new to finite difference method and I am just introduced to methods of solving differential equation using finite difference method via sparse matrix method. I find that the main idea is to ...
Hari Sam's user avatar
2 votes
0 answers
67 views

Order of local error when integrating ODE with discontinous derivatives

I'm working with ODEs, $$\dot{x} = f(x, t),$$ where the (higher) derivatives of the right-hand side have discontinuities. In particular, $f(x, t)$ is obtained by interpolation of discrete samples, and ...
Tor's user avatar
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3D Quadrature schemes with points on boundary

In one dimension there are two types of quadrature schemes. asymmetric rules like Newton-Cotes like formulas (Trapezodi, Simpson), and Clenshaw-Curtis place sampling points on boundary of the ...
Prokop Hapala's user avatar
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1 answer
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What happens to the $O(\cdot)$ terms when we implement the Leapfrog Integration algorithm in a programming language?

Integration Algorithms The Verlet leapfrog algorithm is an economical version of the basic algorithm, in that it needs to store only one set of positions and one set of velocities for the atoms, and ...
user366312's user avatar
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1 answer
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finding weak form of nonlinear differential equation for FEM simulation

The following is the well-known nonlinear differential equation for director's distribution at static equilibrium in liquid crystal displays(LCD). I want to obtain weak form of the given differential ...
Hari Sam's user avatar
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1 answer
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'Integral2' error in MATLAB for invalid integrand

Here is the code that I am trying to run: ...
vidyarthi's user avatar
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Solving coupled 2nd-order differential equation

I would appreciate it if you could help me solve the following coupled equation numerically $$ [-\frac{1}{2} \partial_r^2 + v_0(r) -E]\psi_{\ell} + v_1(r) \psi_{1-\ell}(r) = 0, $$ where $\ell = 0 , 1$ ...
Ghoti's user avatar
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Unable to solve numerically this system of differential equation

I'm trying to obtain the graph of x(y) from the following system : Therefore I tried to solve this system using an Euler Method : ...
Mipix's user avatar
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How to minimize a numerical integration in python?

I need some help to minimize a numerical integration. It's about a classical problem in physics (hydrogen atom). It can be solved analytically but I need to solve it numerically in Python. We have an ...
Rubens Filho's user avatar
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118 views

Am I doing leapfrog integration correctly?

I wrote this minimal example to examine the Leapfrog integration algorithm. However, I am not sure it is the correct algorithm, and the listing is giving the correct output. Is this the Leapfrog ...
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Matching the limits of integration with the proper variables in a complicated case when using scipy.integrate.nquad

I need to integrate expressions containing powers of the function: ...
ale victor's user avatar