# Questions tagged [method-of-lines]

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• 319
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### Method of Lines for Wave Equation with Periodic Bounday Condition

I am trying to solve, using the method of lines in Matlab, the wave equation IVP: \begin{cases} \frac{\partial^2 v}{\partial t^2} = \frac{\partial^2 v}{\partial x^2} \\ v(x, 0) = e^{-x^2} &...
• 11
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### Problem with solving coupled ODE and DAE equations with mass matrix (Error using daeic12 (line 77) This DAE appears to be of index greater than 1)

I am trying to solve 6 ODE equations coupled with 1 DAE one. The ODE equations have been discritized in space domain and ode15s MATLAB solver is used to solve the equations in time domain. I have ...
• 1
182 views

### Are spatial boundary conditions required for PDEs discretized with Method of Lines?

As far as I understand, you need to define boundary conditions in time and space to select a unique solution to a PDE and make it solvable. However, in ODEs I only need to specific the initial value ...
• 231
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### Method of Lines: How to simplify Jacobian with periodic BCs?

Consider the advection equation $$\frac{\partial u}{\partial t}+c(x)\frac{\partial u}{\partial x}=0.$$ With periodic boundary condtitions in $x$ with period $L$, i.e. $u(x,t)=u(x+L,t)$ and initial ...
• 219
251 views

### Method of Lines (MOL) for coupled PDEs

I am trying to solve the set of equations posted here- Solving the heat diffusion equation with source term One of the methods I have learnt to solve second order PDEs is the 'method of lines', where ...
87 views

### How to increase the stability of a DAE solver?

I am trying to solve a set of linear PDEs of the form $$F\left(\vec{y},\frac{\partial \vec{y}}{\partial x},\frac{\partial^2 \vec{y}}{\partial x^2},\frac{\partial \vec{y}}{\partial t}\right)=0.$$ To ...
• 219
164 views

• 21
1 vote
487 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 ...
13k 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 ...
• 568
1 vote
113 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 ...
• 568
130 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 ...
• 41
224 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 ...
• 73
1 vote
303 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 ...
• 73
1k 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 ...
• 73
1 vote
1k 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....
• 73
1 vote
227 views

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