The resulting block diagram looks nothing like the original system representation. Several pages of derivations are required just to translate a free-body diagram to a differential equation.

If you pull twice as hard on a spring, it stretches twice as far. However, when we introduce very large forces or complicated ...

Understanding the Finite-Difference Method (FDM) The finite-difference method is the most direct approach to discretizing partial differential equations.

The plots below illustrate the difference between computations on a moving mesh (left) and a fixed grid (right), both with the same number of grid points. The partial differential differential ...

Abstract This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, for parabolic partial differential equations (PDEs) of ...

Modern modeling approaches for circuit simulation such as the modified nodal analysis (MNA) lead to differential-algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical ...