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  2. Method of lines - Wikipedia

    en.wikipedia.org/wiki/Method_of_lines

    Method of lines - the example, which shows the origin of the name of method. The method of lines (MOL, NMOL, NUMOL [1] [2] [3]) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized.

  3. Numerical methods for ordinary differential equations

    en.wikipedia.org/wiki/Numerical_methods_for...

    In this section, we describe numerical methods for IVPs, and remark that boundary value problems (BVPs) require a different set of tools. In a BVP, one defines values, or components of the solution y at more than one point. Because of this, different methods need to be used to solve BVPs.

  4. Relaxation (iterative method) - Wikipedia

    en.wikipedia.org/wiki/Relaxation_(iterative_method)

    Relaxation methods were developed for solving large sparse linear systems, which arose as finite-difference discretizations of differential equations. [2] [3] They are also used for the solution of linear equations for linear least-squares problems [4] and also for systems of linear inequalities, such as those arising in linear programming. [5 ...

  5. 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 ...

  6. Numerical Methods for Partial Differential Equations - Wikipedia

    en.wikipedia.org/wiki/Numerical_Methods_for...

    Numerical Methods for Partial Differential Equations is a bimonthly peer-reviewed scientific journal covering the development and analysis of new methods for the numerical solution of partial differential equations. It was established in 1985 and is published by John Wiley & Sons.

  7. Method of characteristics - Wikipedia

    en.wikipedia.org/wiki/Method_of_characteristics

    In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations , though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation .

  8. Partial differential equation - Wikipedia

    en.wikipedia.org/wiki/Partial_differential_equation

    In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.

  9. Stencil (numerical analysis) - Wikipedia

    en.wikipedia.org/wiki/Stencil_(numerical_analysis)

    The Crank–Nicolson stencil for a 1D problem. In mathematics, especially the areas of numerical analysis concentrating on the numerical solution of partial differential equations, a stencil is a geometric arrangement of a nodal group that relate to the point of interest by using a numerical approximation routine.