Analytic solution Definition and 5 Discussions

In mathematics, a closed-form expression is a mathematical expression expressed using a finite number of standard operations. It may contain constants, variables, certain "well-known" operations (e.g., + − × ÷), and functions (e.g., nth root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation, or integration. The set of operations and functions admitted in a closed-form expression may vary with author and context.

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  1. Dario56

    I Why is it Impossible to Solve the Three Body Problem Analytically?

    Three (many) body problems where three or many bodies (particles) interact are impossible to solve analytically. First one appeared in classical mechanics where equations of motion of planets were tried to be found by applying Newton's 2nd law for system of planets and stars interacting via...
  2. A

    Modeling analytical solution of 1D heat equation

    I am trying to write code for analytical solution of 1D heat conduction equation in semi-infinite rod. The analytical solution is given by Carslaw and Jaeger 1959 (p305) as $$ h(x,t) = \Delta H .erfc( \frac{x}{2 \sqrt[]{vt} } ) $$ where x is distance, v is diffusivity (material property) and t...
  3. P

    What is the scope of analytical research in astrophysics?

    Nowadays much of the community of astronomy and astrophysics is focused on simulations and data analysis. Thus people, who do not have access to grids and data, must resort to analytical analysis. What are the challenging areas of astronomy and astrophysics that rely on analytical workout rather...
  4. dylanreynolds1

    Computational General Relativity

    Hello all, first post. I have come here to get second opinions on the program I have written to compute the Einstein Tensor (the Riemann Tensor and Ricci Tensor). I enjoy looking for solutions to the Einstein Field Equations, however computing them by hand is not realistic. I decided to write a...
  5. kostoglotov

    Multiple Integral Challenge Question, no solution in guide

    I have what I think is a valid solution, but I'm not sure, and when I try to check the answer approximately in Matlab, I don't get a verified value, and I'm not sure if my analytic solution or my approximation method in Matlab is at fault. 1. Homework Statement Evaluate the integral...