Partial Differential Equations Web Application

This web application solves various linear and nonlinear partial differential equations in 1, 2 and 3 dimensions using finite element and finite difference methods to approximate the solution in each case. The equations usually involve an unknown for fonction of more than two variables with its partial derivatives.  They have the following general form.

Partial differential equations are used in various scientific and engineering modeling and analysis studies  for research and development of new technologies. Partial differential equations are ubiquitous in mathematically oriented scientific fields, such as physics and engineering. For instance, they are foundational in the modern scientific understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics (Schrödinger equation, Pauli equation etc.). They also arise from many purely mathematical considerations, such as differential geometry, stochastic analysis and the calculus of variations; among other notable applications, they are the fundamental tool in the proof of the Poincaré conjecture from geometric topology.
In this application, equations are mainly second order equations and can be classified as Parabolic, Elliptic or Hyperbolic, and are defined using templates from the menu above.
For instance in order to solve a Linear Parabolic Equation on the interval [A,B] from time t=s to t=T, we use the following template:

Note that this web application supports elementary functions, their syntax is similar as in C++ math.h library, i.e. abs(x), sin(x), cos(x), exp(x), log(x), sqrt(x), tan(x), acos(x), asin(x), atan(x),...etc.