Mathematica 7 can solve nonlinear second-order partial differential equations (PDEs) but often requires numerical methods due to the scarcity of known solutions. Users should start with simple examples that have closed-form solutions to understand the syntax and functionality of DSolve. For more complex equations, such as groundwater flow equations, numerical methods like Finite Element Method (FEM) or Finite Difference Method (FDM) should be employed. Initial and boundary conditions are essential for accurate modeling in these cases.
PREREQUISITESStudents and researchers in applied mathematics, particularly those working on groundwater modeling and numerical solutions of partial differential equations.
Mathematica can solve any PDE for which a solution is known. However, there are going to be very few, if any, known solutions for nonlinear 2nd order PDE's. You will probably need to do it numerically.abbeyNewton said:hello, i just want to ask if mathematica 7 can solve nonlinear second order partial differential equations. i tried solving it with DSolve but it kept on giving me the question back as the output...please is there any way or syntax for solving it on mathematica 7?...thanks for any suggestions.