Partial Differential Equations Web Application

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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 that 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.
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:


Click the enter button to fill in  the coefficents and initial conditions and then press the solve button.

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.

 

     Download  the Solution Data Output or  Graph

Output