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  2. Numerical Methods for Partial Differential Equations

    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.

  3. 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.

  4. 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.

  5. 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 .

  6. Explicit and implicit methods - Wikipedia

    en.wikipedia.org/wiki/Explicit_and_implicit_methods

    Explicit and implicit methods are approaches used in numerical analysis for obtaining numerical approximations to the solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes.

  7. Stencil (numerical analysis) - Wikipedia

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

    Stencils are the basis for many algorithms to numerically solve partial differential equations (PDE). Two examples of stencils are the five-point stencil and the Crank–Nicolson method stencil. Stencils are classified into two categories: compact and non-compact , the difference being the layers from the point of interest that are also used ...

  8. Finite difference method - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_method

    The scheme is always numerically stable and convergent but usually more numerically intensive than the explicit method as it requires solving a system of numerical equations on each time step. The errors are linear over the time step and quadratic over the space step: Δ u = O ( k ) + O ( h 2 ) . {\displaystyle \Delta u=O(k)+O(h^{2}).}

  9. 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 ...