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  2. Numerical methods for ordinary differential equations - Wikipedia

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

    where is a function : [,), and the initial condition is a given vector. First-order means that only the first derivative of y appears in the equation, and higher derivatives are absent. Without loss of generality to higher-order systems, we restrict ourselves to first-order differential equations, because a higher-order ODE can be converted ...

  3. List of nonlinear ordinary differential equations - Wikipedia

    en.wikipedia.org/wiki/List_of_nonlinear_ordinary...

    Differential equations are prominent in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations.

  4. Ordinary differential equation - Wikipedia

    en.wikipedia.org/wiki/Ordinary_differential_equation

    Some ODEs can be solved explicitly in terms of known functions and integrals. When that is not possible, the equation for computing the Taylor series of the solutions may be useful. For applied problems, numerical methods for ordinary differential equations can supply an approximation of the solution.

  5. Finite difference method - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_method

    For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).

  6. Direct multiple shooting method - Wikipedia

    en.wikipedia.org/wiki/Direct_multiple_shooting...

    Even stable and well-conditioned ODEs may make for unstable and ill-conditioned BVPs. A slight alteration of the initial value guess y 0 may generate an extremely large step in the ODEs solution y(t b; t a, y 0) and thus in the values of the function F whose root is sought. Non-analytic root-finding methods can seldom cope with this behaviour.

  7. JoJo Siwa 'Pledged' Not to Share Dating Life Publicly After ...

    www.aol.com/jojo-siwa-pledged-not-share...

    "You know, it's interesting. My mom always used to tell me, 'The whole world doesn't need to know everything. JoJo. You can keep some things a secret.'

  8. Fed Chair Powell says he won't resign if Trump asks him to ...

    www.aol.com/fed-chair-powell-says-wont-202841242...

    Federal Reserve Chair Jerome Powell said he won't step down if President-elect Donald Trump, who has previously criticized Powell's performance, asks him to resign.

  9. Fact or Fiction: Joel Embiid and the Philadelphia 76ers are ...

    www.aol.com/sports/fact-fiction-joel-embiid...

    No team would ever ask for this. Except for the Sixers, who just signed up for four more years of it. Determination: Fact. Joel Embiid and the 76ers are in for a long season. Show comments.