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  2. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

  3. Linear multistep method - Wikipedia

    en.wikipedia.org/wiki/Linear_multistep_method

    Numerical methods for ordinary differential equations approximate solutions to initial value problems of the form ′ = (,), =.. The result is approximations for the value of () at discrete times : = +, where is the time step (sometimes referred to as ) and is an integer.

  4. List of open-source software for mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_open-source...

    The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations.

  5. Numerical methods for ordinary differential equations - Wikipedia

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

    Ernst Hairer and Gerhard Wanner, Solving ordinary differential equations II: Stiff and differential-algebraic problems, second edition, Springer Verlag, Berlin, 1996. ISBN 3-540-60452-9. (This two-volume monograph systematically covers all aspects of the field.) Hochbruck, Marlis; Ostermann, Alexander (May 2010). "Exponential integrators".

  6. Euler method - Wikipedia

    en.wikipedia.org/wiki/Euler_method

    The next step is to multiply the above value by the step size , which we take equal to one here: h ⋅ f ( y 0 ) = 1 ⋅ 1 = 1. {\displaystyle h\cdot f(y_{0})=1\cdot 1=1.} Since the step size is the change in t {\displaystyle t} , when we multiply the step size and the slope of the tangent, we get a change in y {\displaystyle y} value.

  7. Bogacki–Shampine method - Wikipedia

    en.wikipedia.org/wiki/Bogacki–Shampine_method

    The Bogacki–Shampine method is implemented in the ode3 for fixed step solver and ode23 for a variable step solver function in MATLAB (Shampine & Reichelt 1997). Low-order methods are more suitable than higher-order methods like the Dormand–Prince method of order five, if only a crude approximation to the solution is required.

  8. Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta_methods

    This can be contrasted with implicit linear multistep methods (the other big family of methods for ODEs): an implicit s-step linear multistep method needs to solve a system of algebraic equations with only m components, so the size of the system does not increase as the number of steps increases. [27]

  9. Jacobi method - Wikipedia

    en.wikipedia.org/wiki/Jacobi_method

    In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in.