Finite difference method Definition and 65 Threads
In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points.
Finite difference methods convert ordinary differential equations (ODE) or partial differential equations (PDE), which may be nonlinear, into a system of linear equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently which, along with their relative ease of implementation, has led to the widespread use of FDM in modern numerical analysis.
Today, FDM are one of the most common approaches to the numerical solution of PDE, along with finite element methods.
How do I use the finite difference method with M = N = 20 to obtain a plot of the solution of
\nabla2u = 1, 0 < x < 1, 0 < y < 1,
u(x,0) = x(1-x), u(x,1) = x(1-x), 0 \leq y \leq 1,
u(0,y) = 0, u(1,y) = 0, 0 \leq y \leq 1.
Hi
I am trying to solve a nonlinear differential equation with the use of the finite difference method and the Newton-Raphson method. Is there anyone that knows where I can find some literature about the subject?
I am familiar with the use of the finite difference method, when solving...
Hi
The equation is:
\frac{dP}{dt}-A*\frac{{d}^2P}{dx^2}-B*\frac{dC}{dt}=0
dP/dt=A*d2P/dx^2 was solved using a finite difference method. If the function C(x,t) is known, is it possible to solve the whole equation by using the finite difference solution as a supplement to the complete solution...
Homework Statement
I have uploaded the problem statement and corresponding programs.
Reader is the problem statement
Reader1 is another file that is suppose to help
Homework Equations
I'm just having trouble getting started. I can do the analytical part on paper, but I don't know...
I'm going to take a finite difference linear and non-linear PDE course next semester. I'm wondering how enjoyable the material is, and how difficult it may be. I'm actually looking forward to the fact there may only be one test throughout the semester, if any, and it's a mid-term. The rest of...
To the moderator: please move this to the section on differential equations if you think it would be better there.
I'm looking at a reaction-diffusion equation of the form
\frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} + f(u),
where, e.g., f(u) = u(1-u) for the...
Fiber Grating Using Finite Difference Method
I have to solve the Fiber grating coupled-equations using FDM. These equations are coupled each other and strange inital conditions. That means ode45 from the MATLAB library function doesn't work here!
I am totally fresh in numerical analysis...
1) Using a similarity variable, the boundary layer equations for a two-dimensional, incompressible flow over a flat plate can be written below:
2f'''+ff''=0
The boundary conditions are:
a) f ' (0) = 0, no slip at the wall
b) f(0)=0, solid wall
c) f ' (n) goes 1 as n goes infinity...
1) Using a similarity variable, the boundary layer equations for a two-dimensional, incompressible flow over a flat plate can be written below:
2f'''+ff''=0
The boundary conditions are:
a) f ' (0) = 0, no slip at the wall
b) f(0)=0, solid wall
c) f ' (n) goes 1 as n goes...
computer engineering and mathematics,do you understand both of them?if u understand pls meet me.ı have a homework contains MATLAB course.ı can not write a program
:confused: my question y''(t)=-exp(-2t)+5y(t) accuracy on 5*10^(-3) by finite difference method and this question's MATLAB program. is there anyone who can do it ? it is very important for me.ı can not do and write a program in matlab.ı am a student ,my department is mathematics but ı can not...
I am curious to know if anyone has a program that will solve for 2-D Transient finite difference I have an assignment in a heat transfer class and I am supposed to use Matlab to solve for this. The governing equation (given in the attachement) is to solve using finite difference method using...
I am curious to know if anyone has a program that will solve for 2-D Transient finite difference I have an assignment in a heat transfer class and I am supposed to use Matlab to solve for this. The governing equation given here is to solve using finite difference method using matlab.
In...
I am curious to know if anyone has a program that will solve for 2-D Transient finite difference.
I have a project in a heat transfer class and I am supposed to use Matlab to solve for this. However, when I took the class to learn Matlab, the professor was terrible and didnt teach much at...