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  2. Finite difference method - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_method

    The finite difference method relies on discretizing a function on a grid. To use a finite difference method to approximate the solution to a problem, one must first discretize the problem's domain. This is usually done by dividing the domain into a uniform grid (see image).

  3. Numerical solution of the convection–diffusion equation

    en.wikipedia.org/wiki/Numerical_solution_of_the...

    For time-dependent equations, a different kind of approach is followed. The finite difference scheme has an equivalent in the finite element method (Galerkin method). Another similar method is the characteristic Galerkin method (which uses an implicit algorithm). For scalar variables, the above two methods are identical.

  4. Crank–Nicolson method - Wikipedia

    en.wikipedia.org/wiki/Crank–Nicolson_method

    In numerical analysis, the Crank–Nicolson method is a finite difference method used for numerically solving the heat equation and similar partial differential equations. [1] It is a second-order method in time. It is implicit in time, can be written as an implicit Runge–Kutta method, and it is numerically stable.

  5. FTCS scheme - Wikipedia

    en.wikipedia.org/wiki/FTCS_scheme

    In numerical analysis, the FTCS (forward time-centered space) method is a finite difference method used for numerically solving the heat equation and similar parabolic partial differential equations. [1] It is a first-order method in time, explicit in time, and is conditionally stable when applied to the heat equation.

  6. Alternating-direction implicit method - Wikipedia

    en.wikipedia.org/wiki/Alternating-direction...

    Stencil figure for the alternating direction implicit method in finite difference equations. The traditional method for solving the heat conduction equation numerically is the Crank–Nicolson method. This method results in a very complicated set of equations in multiple dimensions, which are costly to solve.

  7. Metal casting simulation - Wikipedia

    en.wikipedia.org/wiki/Metal_casting_simulation

    Finite difference method (FDM): This method is based on differential equations of heat and mass transfer, which are approximated using finite difference relationships. [18] The advantage of the FDM is its simplicity and the ability to simplify the solution of multidimensional problems.

  8. Von Neumann stability analysis - Wikipedia

    en.wikipedia.org/wiki/Von_Neumann_stability_analysis

    A finite difference scheme is stable if the errors made at one time step of the calculation do not cause the errors to be magnified as the computations are continued. A neutrally stable scheme is one in which errors remain constant as the computations are carried forward. If the errors decay and eventually damp out, the numerical scheme is said ...

  9. CFD in buildings - Wikipedia

    en.wikipedia.org/wiki/CFD_in_buildings

    CFD technique can be used for the analysis of heat transfer in each part of a building. CFD technique finds the solution by following ways: Discretization of the governing differential equation using numerical methods (Finite difference method has been discussed). Solve the discretized version of equation with high performance computers.