Concepts inA test package for Sturm-Liouville solvers
Sturm¿Liouville theory
In mathematics and its applications, a classical Sturm¿Liouville equation, named after Jacques Charles François Sturm (1803¿) and Joseph Liouville (1809¿), is a real second-order linear differential equation of the form where y is a function of the free variable x. Here the functions p(x) > 0, q(x), and w(x) > 0 are specified at the outset.
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Ordinary differential equation
In mathematics, an ordinary differential equation (abbreviated ODE) is an equation containing a function of one independent variable and its derivatives. There are many general forms an ODE can take, and these are classified in practice (see below). The derivatives are ordinary because partial derivatives only apply to functions of many independent variables.
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Solver
A solver is a generic term indicating a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculate their solution. In a solver, the emphasis is on creating a program or library that can easily be applied to other problems of similar type.
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Fortran
Fortran (previously FORTRAN) is a general-purpose, procedural, imperative programming language that is especially suited to numeric computation and scientific computing.
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Eigenvalues and eigenvectors
The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain parallel to the original vector. For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector is scaled when multiplied by the matrix. The prefix eigen- is adopted from the German word "eigen" for "self" in the sense of a characteristic description. The eigenvectors are sometimes also called characteristic vectors.
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