# Questions tagged [explicit-methods]

The tag has no usage guidance.

25 questions
Filter by
Sorted by
Tagged with
53 views

### how can I plot specific iterations?

I have made this code for an explicit Euler method but I want to plot only the 0,1,25,50 iterations not all of them.How can I do it? ...
100 views

### 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....
156 views

### 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 ...
88 views

### 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 ...
163 views

### 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 ...
152 views

### Finite difference - Explicit / Implicit / Crank Nicolson - Does the implicit method require the least memory?

Examine a dynamic 2D heat equation $\dot{u} = \Delta u$ with zero boundary temperature. A standard finite difference approach is used on a rectangle using a $n\times n$ grid. For the resulting linear ...
310 views

### ODE: should Euler implicit be more accurate than Euler explicit for a given computational step?

I am aware than Euler explicit is conditionally stable, and Euler implicit is unconditionally stable. And I am aware that it is probably pointless to use Euler implicit with a small computational step ...
122 views

### Euler Method Instability. Why?

I am currently enjoying writing computational codes as a hobby. Right now I've worked out an Euler method and results are pretty good with up to $x=1$. Over $x=1$, instability starts to kick in. May I ...
104 views

### Stability Criteria for Numerical Solution of Windkessel Ordinary Differential Equation

I'm trying to solve this equation (Windkessel equation) numerically as: $$C \frac{d P}{d t} + \frac{P}{R} = Q(t)$$ Where $C$ is compliance, $R$ is resistance, $P$ is pressure, and $Q(t)$ is a known ...
290 views

### Solving PDE implicitly or explicitly depending on stiffness

I've got a system of several PDEs for a multitude of parts which represent real hydraulic parts like pipes or thermal energy storages. Each of these parts may have an arbitrary number of nodes and/or ...
58 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 ...
765 views

### Finite Difference Method Limitations/Stability Criteria

Is it possible to solve an equation with only a single derivative such as: $$\frac{\partial U(x,t)}{\partial t} = A - BU(x,t)$$ with finite difference methods? I ask as I am trying to solve the ...
174 views

### From explicit to implicit SSP Runge-Kutta time discretization for DG

In Hesthaven book (Nodal Discontinuous Galerkin Methods) he uses SSP Runge-Kutta time method which is explicit. How can I change the explicit RK to an implicit one?
152 views

### Stability of the explicit MacCormack Scheme to solve the Navier Stokes equations with Wilcox's K-Omega Turbulence Model

I am solving turbulent pipe flow with an explicit MacCormack scheme and Wilcox k-omega model. The laminar version of the code had three distinct stability criteria which worked fine after ...
324 views

8k views

### What is the difference between implicit FEM and explicit FEM?

What is the difference between explicit FEM and implicit FEM exactly? According to the post here, it seems that the only difference is whether implicit or explicit time integration is used. As I ...
574 views

### Stability of forward euler method

I am trying to understand the stability of the forward Euler method. I read there's a model problem to see the stability. $$y'(t) = \lambda y(t) \qquad t \in (0, \infty)$$ $$y(0) = 1$$ then the book ...
555 views

### Runge-Kutta and Reusing Datapoints

I am trying to implement the fourth order Runge-Kutta method for solving a first order ODE in Python i.e. $\frac{dy}{dx} = f(x,y)$. I understand how the method works, but am trying to write an ...