Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [method-of-lines]

The tag has no usage guidance.

-1
votes
0answers
60 views

Understanding how to solve DAE

I am solving the following pde that is discretized in space using method of lines, in MATLAB using ode15s. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2}-v\frac{\partial C}{\...
1
vote
2answers
128 views

Mass conservation in 1d diffusion by method of lines

I am solving the 1D diffusion equation by discretization using the method of lines. My problem is that I don't manage to ensure mass conservation. I have read many similar questions about the topic ...
2
votes
2answers
268 views

Neumann boundary conditions diffusion equations methods of lines

I want to solve the diffusion equation using the method of lines with Neumann boundary conditions $$ \frac{\partial p}{\partial t}=\frac{\partial^2p}{\partial x^2}\\ \frac{\partial p}{\partial x}(x=0)=...
1
vote
2answers
262 views

implementation of method of line and Runge-Kutta to the given equation

$$\frac{d^2 u}{dx^2} +A \frac{d^2}{dx^2}\left(\frac{du}{dt}\right)=B $$ I want to solve the equation given above. I need to first discretize it by the Method of Lines and then evolve the resulting ...
1
vote
0answers
73 views

Methods to approximate discretized derivatives in PDEs

When solving a general PDE such as $$ \frac {\partial ^2 E}{\partial t ^2} = \frac {\partial ^2 E}{\partial z ^2} - \frac {\partial E}{\partial z} $$ this equation can be solved by the method of ...
2
votes
2answers
2k views

Understanding the Courant–Friedrichs–Lewy condition

I understand these equations in particular can be solved easily without use of computational methods. Although right now I am concerned with trying to solve these equations using numerical integration ...
1
vote
1answer
82 views

Classification of method for solving PDEs

If I have a system of equations as follows (where $i = \sqrt{-1}$): $$ \frac {\partial A}{\partial t} = iA^*B - A \tag{1} \\ $$ $$ \frac {\partial B}{\partial z} = AB^* - B \tag{2} $$ Using the ...
1
vote
0answers
121 views

Using backward difference approximations for higher order derivatives

I am trying to solve a system of equations and have a question regarding the validity of my approach when implementing a fifth-order Cash-Karp Runge-Kutta (CKRK) embedded method with the method of ...
3
votes
2answers
91 views

numerical approach for system of non-linear partial-ordinary differential equations

I am interested in the numerical solution of the following system of non-linear partial-differential algebraic equations, where the independent variables are $X$ and $T$, representing non-dimensional ...
-3
votes
1answer
199 views

How can I solve stiff equations by method of line (MOL)?

I want to solve 7 coupled equations.I use method of line(MOL) and discrete the equation in Length and radius and convert them to a system of ODEs in time.and use ode15s to solve them in MATLAB. But an ...
1
vote
3answers
213 views

solving PDEs in MATLAB

I want to solve 3 coupled equations. I converted them to a system of odes in time and discrete it in Length and radius. Now I have a problem in one of the equations in first point. Because in this ...
2
votes
1answer
602 views

Solving DAE with higher index

I want to solve 7 coupled differential equations in MATLAB. I used the method of lines (MOL) to convert them to a system of DAEs. I then attempted to solve this system using ode15s. Unfortunately an ...
1
vote
1answer
757 views

How can I solve coupled equations by the method of line(MOL)?

I want to solve 3 coupled PDEs equations. They depend on time, radius and length. I used the method of lines (MOL) and converted them to a system of ODEs in time. Now I want to solve them using MATLAB....
0
votes
1answer
154 views

How can i define algebraic equation in differential function in MATLAB?

I want to solve 7 pde's that are functions of time, radius(j) and length(i). I used the method of lines and converted them to a system of odes in time and it becomes something like this: $$dy/dt=((y(i,...
0
votes
1answer
137 views

What is the meaning of this error in MATLAB?

Warning: Failure at t=6.137539e-04. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.734723e-18) at time t. In ode15s (line 730) In ...
0
votes
1answer
516 views

Solving coupled differential equations and Algebraic equation in MATLAB

I want to solve a system of 7 coupled differential equations and 1 algebraic equation in MATLAB with the method of lines. I could do it for each independent equation with some assumptions, but I can'...
4
votes
1answer
121 views

transverse component for multidimensional advection in method of lines

So I inherited from some people a code that solves the advection-diffusion-reaction equation for a particular system. The original code was first implemented in 1D which worked fine in cartesian ...
1
vote
0answers
54 views

Method of lines: explanation for high precision low resolution flux and vice versa

Could someone please explain what is meant with e.g high precision low resolution flux. Does it mean, that I use some higher order method (still first order) but with a more complex stencil and ...
2
votes
2answers
82 views

Integro-differential PDE and method of lines

Let us consider the following equation : $$\partial_t u = \Delta_x u + K*u$$ where $K$ is a smooth kernel, $u(x,t)$ is the unknown and $x$ is in $\Omega$ a domain in 1d or 2d. I want to numerically ...
9
votes
1answer
245 views

Can the method of lines be used to discretize all PDEs?

I have found that the method of lines is a very natural way to think about the discretization of PDE's. Therefore I always default to that mindset when presented with a new set of equations. I have ...
2
votes
0answers
211 views

1 D Diffusion equation FDM with different layers

I'm trying to solve this particular equation $\frac{\partial u}{\partial t} = \frac{\partial}{\partial x} \big[D_{i}(x)\frac{\partial u}{\partial x} \big] + S(x,t)$ where the $i$ index denotes ...
-1
votes
1answer
85 views

Can you give some information for rothe method [closed]

I want to learn a numerical method for PDEs other than finite difference method. After some research on internet i have found Rothe method and it looks interesting to me. Unfortunately, i couldn't ...
2
votes
0answers
129 views

Solvers for stiff initial value ODEs with sparse Jacobian

What ODE solvers are optimized for solving stiff systems with sparse Jacobian? Such systems appear, for instance, when a parabolic PDE is discretized in space using typical finite difference or finite ...
-1
votes
1answer
101 views

Libraries with the method of lines for parabolic PDEs [closed]

Could you please advise some programs or libraries for solving parabolic PDEs (or its systems) in 1D, 2D and 3D, for example, with the method of lines? The system of parabolic PDEs can be nonlinear in ...
1
vote
3answers
1k views

Applying the method of lines to parabolic PDEs: references and software

Could you please advise some literature about the numerical method of lines (MOL) for parabolic PDEs? It is a method of solving PDEs with discretizing only by space but not by time. A system of ODEs ...
2
votes
1answer
365 views

Can the method of lines technique be used to solve a ODE directly for the steady-state value?

Say we have a discretised a coupled nonlinear system of two PDEs to give a system of ODEs which approximates the original system, $$ \frac{\partial u}{\partial t} = F_1(t,\boldsymbol{u,v}) \\ \frac{\...
4
votes
1answer
981 views

Confusion regarding the Adam-Moulton and Backwards Differentiation Formula (BDF) of the VODE solver

I am exploring the Method of Lines as a way of time stepping semi-discretised PDEs with ODE time-integration solvers. For an excellent introduction to this technique see the scholarpedia.org article. ...