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  2. Numerical methods for ordinary differential equations - Wikipedia

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

    This is the Euler method (or forward Euler method, in contrast with the backward Euler method, to be described below). The method is named after Leonhard Euler who described it in 1768. The Euler method is an example of an explicit method. This means that the new value y n+1 is defined in terms of things that are already known, like y n.

  3. How to Solve It - Wikipedia

    en.wikipedia.org/wiki/How_to_Solve_It

    How to Solve It (1945) is a small volume by mathematician George Pólya, describing methods of problem solving. [ 1 ] This book has remained in print continually since 1945.

  4. Stencil (numerical analysis) - Wikipedia

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

    The finite difference coefficients for a given stencil are fixed by the choice of node points. The coefficients may be calculated by taking the derivative of the Lagrange polynomial interpolating between the node points, [3] by computing the Taylor expansion around each node point and solving a linear system, [4] or by enforcing that the stencil is exact for monomials up to the degree of the ...

  5. Linear multistep method - Wikipedia

    en.wikipedia.org/wiki/Linear_multistep_method

    Iterative methods such as Newton's method are often used to solve the implicit formula. Sometimes an explicit multistep method is used to "predict" the value of +. That value is then used in an implicit formula to "correct" the value. The result is a predictor–corrector method.

  6. Conjugate residual method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_residual_method

    The conjugate residual method is an iterative numeric method used for solving systems of linear equations. It's a Krylov subspace method very similar to the much more popular conjugate gradient method, with similar construction and convergence properties. This method is used to solve linear equations of the form

  7. Shoelace formula - Wikipedia

    en.wikipedia.org/wiki/Shoelace_formula

    Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]

  8. Conjugate gradient method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_gradient_method

    The conjugate gradient method with a trivial modification is extendable to solving, given complex-valued matrix A and vector b, the system of linear equations = for the complex-valued vector x, where A is Hermitian (i.e., A' = A) and positive-definite matrix, and the symbol ' denotes the conjugate transpose.

  9. Trapezoidal rule (differential equations) - Wikipedia

    en.wikipedia.org/wiki/Trapezoidal_rule...

    In numerical analysis and scientific computing, the trapezoidal rule is a numerical method to solve ordinary differential equations derived from the trapezoidal rule for computing integrals. The trapezoidal rule is an implicit second-order method, which can be considered as both a Runge–Kutta method and a linear multistep method.