Data from an experiment may result in a graph indicating exponential growth. This implies the formula of this growth is \(y = k{x^n}\), where \(k\) and \(n\) are constants. Using logarithms, we can ...

Equations that have more than one unknown can have an infinite number of solutions. For example, \(2x + y = 10\) could be solved by: \(x = 1\) and \(y = 8\) \(x = 2\) and \(y = 6\) \(x = 3\) and \(y = ...

We introduce templates for exponential-asymptotic expansions that, in contrast to matched asymptotic approaches, enable the simultaneous satisfaction of both boundary values in classes of linear and ...

Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

The Characteristics and capabilities of the best codes for solving the initial value problem for ordinary differential equations are studied. Only codes which are readily available, portable, and very ...

Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.

Understanding and improving the impact that Big Tech has on society Technological development is happening faster than ever and changing our lives in fundamental ways. The companies behind all these ...