Problem 51625. Solve an ODE: diffusion problem 2
Problem statement
In the solution of a problem involving diffusion, the following ordinary differential equation arises
where a is a positive constant and primes denote differentiation with respect to the independent variable η. The function f and its derivatives vanish at infinity, and it is subject to the constraint
Write a function to solve this problem—that is, return values of f at specified values of η.
Background
The physical problem involves diffusion of a quantity instantaneously injected at a point—for example, a spill of a contaminant in an initially clean river. The ODE results from transforming the diffusion equation—a partial differential equation in time and a spatial coordinate—with a similarity solution.
Solution Stats
Problem Comments
Solution Comments
Show commentsProblem Recent Solvers5
Suggested Problems
-
1109 Solvers
-
Solve the set of simultaneous linear equations
381 Solvers
-
258 Solvers
-
36 Solvers
-
Number of Even Elements in Fibonacci Sequence
1158 Solvers
More from this Author230
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!