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  2. Partial differential equation - Wikipedia

    en.wikipedia.org/wiki/Partial_differential_equation

    In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.

  3. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    These equations for solution of a first-order partial differential equation are identical to the Euler–Lagrange equations if we make the identification = ˙ ˙. We conclude that the function ψ {\displaystyle \psi } is the value of the minimizing integral A {\displaystyle A} as a function of the upper end point.

  4. Collocation method - Wikipedia

    en.wikipedia.org/wiki/Collocation_method

    In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...

  5. Lectures on Theoretical Physics - Wikipedia

    en.wikipedia.org/wiki/Lectures_on_Theoretical...

    The series includes the volumes Mechanics, Mechanics of Deformable Bodies, Electrodynamics, Optics, Thermodynamics and Statistical Mechanics, and Partial Differential Equations in Physics. Focusing on one subject each semester, the lectures formed a three-year cycle of courses that Sommerfeld repeatedly taught at the University of Munich for ...

  6. Duhamel's principle - Wikipedia

    en.wikipedia.org/wiki/Duhamel's_principle

    Duhamel's principle is the result that the solution to an inhomogeneous, linear, partial differential equation can be solved by first finding the solution for a step input, and then superposing using Duhamel's integral. Suppose we have a constant coefficient, m-th order inhomogeneous ordinary differential equation.

  7. Kolmogorov backward equations (diffusion) - Wikipedia

    en.wikipedia.org/wiki/Kolmogorov_backward...

    The Kolmogorov backward equation (KBE) (diffusion) and its adjoint sometimes known as the Kolmogorov forward equation (diffusion) are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes. Both were published by Andrey Kolmogorov in 1931. [1]

  8. List of nonlinear partial differential equations - Wikipedia

    en.wikipedia.org/wiki/List_of_nonlinear_partial...

    Name Dim Equation Applications Landau–Lifshitz model: 1+n = + Magnetic field in solids Lin–Tsien equation: 1+2 + = Liouville equation: any + = Liouville–Bratu–Gelfand equation

  9. Pierre-Louis Lions - Wikipedia

    en.wikipedia.org/wiki/Pierre-Louis_Lions

    In 1988, François Golse, Lions, Benoît Perthame, and Rémi Sentis studied the transport equation, which is a first-order linear partial differential equation. [GLPS88] They showed that if the first-order coefficients are randomly chosen according to some probability distribution , then the corresponding function values are distributed with ...