Help with finite difference for matlab

Click For Summary
SUMMARY

The discussion focuses on solving the equation Phi = Phi_infinity - Phi_t using the finite difference method in MATLAB. The parameters are defined as Phi_infinity = 1 - e^2 and Phi_t = A(t) * B(e), with A governed by the differential equation dA/dt = -c^2 * A and B defined by 1/e * d/de(edB/de) = -c^2 * B. The initial and boundary conditions are specified as Phi(0) = 0, Phi(0) = 1, and Phi(1) = 0. The problem involves separation of variables to solve the Fourier equation in one dimension.

PREREQUISITES
  • Understanding of finite difference methods in numerical analysis
  • Familiarity with MATLAB programming for numerical simulations
  • Knowledge of differential equations, particularly separation of variables
  • Basic concepts of boundary and initial value problems
NEXT STEPS
  • Study the implementation of finite difference methods in MATLAB
  • Learn about solving differential equations using separation of variables
  • Explore MATLAB's built-in functions for handling boundary value problems
  • Investigate the Fourier equation and its applications in one-dimensional heat transfer
USEFUL FOR

Mathematics students, engineers, and researchers involved in numerical simulations, particularly those working with differential equations and finite difference methods in MATLAB.

lohanlotter
Messages
5
Reaction score
0
I have a question which states that I have to solve Phi using the finite difference method in matlab.

Phi = Phi_infinity - Phi_t

where Phi_infinity = 1 - e^2

and Phi_t = A(t).B(e)

A has the differential for dA/dt = -c^2. A
and B 1/e.d/de(edB/de)=-c^2.B

where e is a separation constant.

I know the boundary and initial condition
at t = 0 Phi = 0
at e = 0 Phi = 1
at e = 1 Phi = 0

Please help I don't know where to start
 
Physics news on Phys.org
What was the original problem? Separation of variables in order to solve the Fourier equation in one dimension? Initial condition of zero everywhere in domain. Then Dirichlet boundary condition at one end to cause the transcience?
 

Similar threads

Matlab report help please (Finite Difference Method)
  • · Replies 5 ·
Replies
5
Views
2K
Engineering Multi-point Boundary Value Problems Using Finite Difference Method
  • · Replies 3 ·
Replies
3
Views
3K
PLL - How to find all the gains of a PI corrector and fix Ki ? MATLAB
  • · Replies 2 ·
Replies
2
Views
2K
Engineering How do I find the transition matrix of this dynamic system?
  • · Replies 18 ·
Replies
18
Views
4K
Undergrad On translation and dilation invariant Lebesgue measure: Folland's text
  • · Replies 2 ·
Replies
2
Views
3K
Engineering Current density calculation in anisotropic ferromagnetic film
  • · Replies 7 ·
Replies
7
Views
2K
Engineering Calculating EMF and Motor Speed for a Compound Wound D.C. Motor
  • · Replies 3 ·
Replies
3
Views
4K
Engineering Concrete Slab Deflection Using Partial Differential Equations
  • · Replies 11 ·
Replies
11
Views
3K
Solving An IVP on Matlab with ODE 45 with different tolerances
  • · Replies 2 ·
Replies
2
Views
2K
Matlab for loop indexing confusion
  • · Replies 1 ·
Replies
1
Views
2K