Questions tagged [explicit-methods]
For questions about explicit differential equation algorithms, that directly relate the next time step of some variable y to some function of y at the current time step.
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Implicit-Explicit Operator Splitting Scheme
I am trying to solve the 2D advection-diffusion equation in cylindrical coordinates:
$$
\frac{\partial c}{\partial t} = D\left(\frac{\partial^2 c}{\partial r^2} + \frac{1}{r}\frac{\partial c}{\partial ...
- 11
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Ways to alleviate my CFL restriction?
I have an advection problem with a sever time stepping restriction. I am using explicit RK type time stepping schemes and standard finite difference so everything is matrix free. Other than going for ...
- 506
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Adding a diffusion term to the MUSCL - Kurganov and Tadmor central scheme
Im currently using a MUSCL scheme with a rusanov flux and Van Leer limiter to simulate the 2d euler equations:
$$ \frac{\partial \rho}{\partial t} + \frac{\partial \rho v_x}{\partial x} + \frac{\...
- 13
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Local truncation error of given implicit 1-step scheme
I'm given the 1-step implicit scheme $$y_{n+1} = y_n + \frac{h}{6}[4f(t_n, y_n) + 2f(t_{n+1}, y_{n+1}) + hf'(t_n, y_n)],$$
where $y'(t) = f(t, y)$, and I'm seeking the scheme's local truncation error. ...
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First-order modified Patankar–Euler scheme (MPE)
Is the first-order Modified Patankar–Euler scheme (MPE) an implicit or explicit method?
Is there an open-source code implementing the MPE scheme for a system of ODEs?
3
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Python code of explicit method of a nonlinear a BVP
I am trying to have a Python code for the following nonlinear BVP:
$$\frac{\partial N}{\partial t}=\frac{\partial^2 N}{\partial x^2}+N(1-N)-\sigma N$$ $$N(0,x)=\sin(2\pi x)$$
$$N(t,0)=0 \hspace{3mm}N(...
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Why do I get an oscillatory solution when applying the implicit trapezoidal method to the linear diffusion equation?
I wish to solve the following equation,
$$\frac{\partial f}{\partial t}=\frac{\partial}{\partial x}\left(D(x)\frac{\partial f}{\partial x}\right)$$
using an exponential integrator.
I discretize this ...
- 97
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Do Explicit Methods Always Require an Analytical Solution
Following some comments from another question I wanted to ask: does an explicit method always require some sort of analytical function/solution?
Let's take Euler for example. You have a function $f$ ...
- 33
2
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Algorithm to numerically determine whether my computed solution for a 1st order ODE is stable/unstable?
We were given an assignment where we had to determine the numerical solution of Dahlquist's equation $\dot x$ = $\lambda x$, ($\lambda$ = $-7$) for time steps ${0.5,0.25,0.125}$ using explicit euler ...
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For implicit schemes, is there any general result that says numerical diffusion increases with smaller timesteps (for CFL<1) as in explicit schemes?
For the first-order explicit upwind scheme, it can be easily shown that, if one keeps the same grid size and progressively decreases the time step below the max allowed one (i.e. below CFL~1) the ...
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Floating point and global error in Euler Method
Inspired by this answer, I tried to understand when floating point errors come into visibility and to check it also comparing the plot of the numerical solution with Explicit Euler with the analytical ...
- 309
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DOP853 integration method is missing (SciPy)
I was checking some integration methods provided by SciPy, in which the DOP853 should be included according to the webpage (https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate....
user33042
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Step size and stability of Euler forward method
I'm trying to calculate the maximum step size that provides stability for the following nonlinear IVP using the Euler forward method:
$u'(t) = -200tu(t)^2,\qquad u_0 = 1, \qquad t\in [0,3]$,
with ...
- 168
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Finite difference methods
I am currently applying the finite difference method to the solution of the diffusion equation.
I think that a problem has occurred, and is as follows, my explicit method is the most accurate when ...
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Stability region of explicit midpoint method
Consider the explicit midpoint method, i.e
$$y_{n+1}-y_{n-1} = 2hf(y_n).$$
I'm asked to apply this method to the linear test equation, $f(y_n) = \lambda y_n,$ in order to find the method's stability ...
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