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  2. Two-body problem in general relativity - Wikipedia

    en.wikipedia.org/wiki/Two-body_problem_in...

    Einstein's equations can also be solved on a computer using sophisticated numerical methods. [1] [2] [3] Given sufficient computer power, such solutions can be more accurate than post-Newtonian solutions. However, such calculations are demanding because the equations must generally be solved in a four-dimensional space.

  3. Prandtl–Glauert transformation - Wikipedia

    en.wikipedia.org/wiki/Prandtl–Glauert...

    The Prandtl–Glauert transformation is a mathematical technique which allows solving certain compressible flow problems by incompressible-flow calculation methods. It also allows applying incompressible-flow data to compressible-flow cases.

  4. Exact solutions in general relativity - Wikipedia

    en.wikipedia.org/wiki/Exact_solutions_in_general...

    Given the difficulty of constructing explicit small families of solutions, much less presenting something like a "general" solution to the Einstein field equation, or even a "general" solution to the vacuum field equation, a very reasonable approach is to try to find qualitative properties which hold for all solutions, or at least for all ...

  5. Solving the geodesic equations - Wikipedia

    en.wikipedia.org/wiki/Solving_the_geodesic_equations

    Solving the geodesic equations is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity, that results in obtaining geodesics. Physically, these represent the paths of (usually ideal) particles with no proper acceleration , their motion satisfying the geodesic equations.

  6. Collocation method - Wikipedia

    en.wikipedia.org/wiki/Collocation_method

    In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...

  7. Spectral method - Wikipedia

    en.wikipedia.org/wiki/Spectral_method

    Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and then to choose the ...

  8. Frobenius solution to the hypergeometric equation - Wikipedia

    en.wikipedia.org/wiki/Frobenius_solution_to_the...

    Since z = 1 − x, the solution of the hypergeometric equation at x = 1 is the same as the solution for this equation at z = 0. But the solution at z = 0 is identical to the solution we obtained for the point x = 0, if we replace each γ by α + β − γ + 1. Hence, to get the solutions, we just make this substitution in the previous results.

  9. Milne-Thomson method for finding a holomorphic function

    en.wikipedia.org/wiki/Milne-Thomson_method_for...

    (,) and (,) are given, 2. (,) is given and () is real on the real axis, 3. only (,) is given, 4. only (,) is given. He is really interested in problems 3 and 4, but the answers to the easier problems 1 and 2 are needed for proving the answers to problems 3 and 4.