Numerical method to solve ODE boundary problem

In summary, there is a second order ordinary differential equation that needs to be solved using a numerical algorithm. The equation includes a parameter 'a' and a function f(x). The goal is to find the eigenvalues, and the routine can be written in MATHLAB or FORTRAN. It is also possible to use MATHEMATICA to solve this type of problem. To find the eigenvalues, one can use the Newton's method to find the zeros of -z^2+z\left(f(z)-\lambda_n\right)=0.
  • #1
zetafunction
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can anyone provide a Numerical algorithm to solve

[tex] -y'' (x) +f(x)y(x) = \lambda _{n} y(x) [/tex]

with the boundary condition [tex] y(0)=y(a)=0 [/tex]

here 'a' is a parameter introduced at hand inside the program

and [tex] f(x) [/tex] is also introduced by hand in the program

i am more interested in getting eingenvalues than obtaining Eigenfunctions

if possible the routine may be in MATHLAB or in FORTRAN thanks

another question can MATHEMATICA solve this kind of eigenvalue problems ??
 
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1. What is a numerical method for solving ODE boundary problems?

A numerical method for solving ODE boundary problems is a mathematical approach that uses numerical techniques to approximate the solution of a differential equation with boundary conditions. This allows for the solution to be computed using a computer algorithm rather than analytical methods.

2. What types of ODE boundary problems can be solved using numerical methods?

Numerical methods can be used to solve a wide range of ODE boundary problems, including linear and non-linear equations, first-order and higher-order equations, and problems with both constant and variable coefficients.

3. How does a numerical method work to solve ODE boundary problems?

A numerical method works by dividing the interval of the problem into smaller subintervals and using a discrete set of points to approximate the solution. These points are then connected using a mathematical formula to create a numerical approximation of the solution.

4. What are the advantages of using numerical methods to solve ODE boundary problems?

There are several advantages to using numerical methods for ODE boundary problems, including the ability to handle complex equations, the ability to obtain accurate solutions within a desired level of error, and the ability to solve problems that do not have analytical solutions.

5. What are some common numerical methods used to solve ODE boundary problems?

Some common numerical methods used to solve ODE boundary problems include Euler's method, Runge-Kutta methods, and finite difference methods. Each method has its own advantages and limitations, and the choice of method depends on the specific problem being solved.

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