Differential Equations Solving
Improvements to solvers for ordinary differential equations (ODEs), partial differential equations (PDEs), and differential algebraic equations (DAEs) continue to strengthen Maple’s world-leading position in numeric and symbolic differential equation solving.
Exact Solutions
Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs)
- New algorithms for solving entire classes of 1st and 2nd order non-linear ODEs and 3rd order linear ODEs for which no systematic algorithms have previously existed
- New transformation techniques for converting equations into forms that Maple can solve; these transformations make it possible for Maple to find solutions to many equations for which there was previously no known solution
- New tools for working with partial differential equations (PDEs), including commands for working with Euler’s operator, conserved currents, and generalized integrating factors, and for computing the general solution for some linear PDE families by using Laplace invariants
Numeric Solutions
Differential Equations (DEs) and Differential Algebraic Equations (DAEs)
Numeric solutions to initial value problems with ordinary differential equations (ODE IVP) and differential algebraic equations (DAE IVP) have many new properties:
- The ability to handle user-defined events: when the event occurs, user-defined actions can be performed or a new event triggered
- Parametric problem definition: a procedure can be formed for a whole class of ODEs or DAEs, then parameters can be adjusted, and different solutions obtained interactively, without the need to set up the problem every time
- Definition of discrete variables as part of the problem description: when combined with events, discrete variables can be used to handle stopping criteria, reset conditions, zero-order holds, and most other events that occur in ODE and DAE system simulation
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