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  2. Logarithmic derivative - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_derivative

    The logarithmic derivative idea is closely connected to the integrating factor method for first-order differential equations. In operator terms, write D = d d x {\displaystyle D={\frac {d}{dx}}} and let M denote the operator of multiplication by some given function G ( x ).

  3. Logarithmic differentiation - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_differentiation

    The technique is often performed in cases where it is easier to differentiate the logarithm of a function rather than the function itself. This usually occurs in cases where the function of interest is composed of a product of a number of parts, so that a logarithmic transformation will turn it into a sum of separate parts (which is much easier ...

  4. Method of undetermined coefficients - Wikipedia

    en.wikipedia.org/wiki/Method_of_undetermined...

    Consider a linear non-homogeneous ordinary differential equation of the form = + (+) = where () denotes the i-th derivative of , and denotes a function of .. The method of undetermined coefficients provides a straightforward method of obtaining the solution to this ODE when two criteria are met: [2]

  5. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d. Derivations also use the log definitions x = b log b (x ...

  6. Numerical methods for ordinary differential equations - Wikipedia

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

    Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. [1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.

  7. 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 (+) + (() +).

  8. Roe solver - Wikipedia

    en.wikipedia.org/wiki/Roe_solver

    The Roe approximate Riemann solver, devised by Phil Roe, is an approximate Riemann solver based on the Godunov scheme and involves finding an estimate for the intercell numerical flux or Godunov flux + at the interface between two computational cells and +, on some discretised space-time computational domain.

  9. First-order partial differential equation - Wikipedia

    en.wikipedia.org/wiki/First-order_partial...

    The general solution to the first order partial differential equation is a solution which contains an arbitrary function. But, the solution to the first order partial differential equations with as many arbitrary constants as the number of independent variables is called the complete integral. The following n-parameter family of solutions