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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]
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.
In numerical analysis, a branch of applied mathematics, the midpoint method is a one-step method for numerically solving the differential equation, ′ = (, ()), =. The explicit midpoint method is given by the formula
The step size is =. The same illustration for = The midpoint method converges faster than the Euler method, as .. Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).
APMonitor: APMonitor is a mathematical modeling language for describing and solving representations of physical systems in the form of differential and algebraic equations. Armadillo is C++ template library for linear algebra; includes various decompositions, factorisations, and statistics functions; its syntax ( API ) is similar to MATLAB.
Symbolic Math Toolbox MathWorks: 1989 2008 9.4(2018a) 2018: $3,150 (Commercial), $99 (Student Suite), $700 (Academic), $194 (Home) including required Matlab: Proprietary: Provides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic. SymPy: Ondřej Čertík 2006 2007 1.13.2: 11 August 2024: Free
The numerical solution of a one-step method depends on the initial condition , but the numerical solution of an s-step method depend on all the s starting values, ,, …,. It is thus of interest whether the numerical solution is stable with respect to perturbations in the starting values.
In the vast majority of cases, the equation to be solved when using an implicit scheme is much more complicated than a quadratic equation, and no analytical solution exists. Then one uses root-finding algorithms, such as Newton's method, to find the numerical solution. Crank-Nicolson method. With the Crank-Nicolson method