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2. Gradient-domain image processing - Wikipedia

   en.wikipedia.org/wiki/Gradient-domain_image...

   The second step is to solve Poisson's equation to find a new image that can produce the gradient from the first step. An exact solution often does not exist because the modified gradient field is no longer conservative , so an image approximating the desired gradient as closely as possible is found.

3. Newmark-beta method - Wikipedia

   en.wikipedia.org/wiki/Newmark-beta_method

   The Newmark-beta method is a method of numerical integration used to solve certain differential equations.It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems.

4. Linear multistep method - Wikipedia

   en.wikipedia.org/wiki/Linear_multistep_method

   Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point. The process continues with subsequent steps to map out the solution.

5. Gassmann's equation - Wikipedia

   en.wikipedia.org/wiki/Gassmann's_equation

   First published in German [1] by Fritz Gassmann, the original work was only later translated in English [2] long after the adoption of the equations in standard geophysical practice. Gassmann's equations remain the most common way of performing fluid substitution—predicting the elastic behaviour of a porous medium under a different saturant ...

6. Newton's method in optimization - Wikipedia

   en.wikipedia.org/wiki/Newton's_method_in...

   The geometric interpretation of Newton's method is that at each iteration, it amounts to the fitting of a parabola to the graph of () at the trial value , having the same slope and curvature as the graph at that point, and then proceeding to the maximum or minimum of that parabola (in higher dimensions, this may also be a saddle point), see below.

7. 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 ...