Contents

---

1. Short presentation
1. PSE for ODEs
   • PSE
   • First contact
2. Goals
3. ODE solvers
   • Non-expert
     1. Troubles
     2. Criticism
     3. Remarks
     4. Available software
   • Expert
     1. Learning
     2. Decision schemes
     3. Remarks
     4. Rules
4. Facilities
5. General schema
6. Platforms and downloading
2. Problems
   1. Theoretical aspects
      • Formulation
      • Stability and solution unicity
      • Stiff systems
   2. Problem description
   3. Interface for problem description
      • Variables
        1. Example
      • Equations
        1. Example
      • Integration interval
        1. Example
      • Initial values
        1. Example
   4. Problem properties
   5. Properties automatic identification
      • Linearity
      • Separability
      • Sparsity
      • Stiffness
      • Computation time
      • Example
   6. Set of problems
      • Test problems
      • Interface facilities
      • Example
3. Methods
   1. Theoretical aspects
      • Formulation
      • Stability and order
      • Linear multistep formulae
      • Runge-Kutta methods
      • Generalized linear multistep methods
      • Generalized Runge-Kutta methods
      • Nonlinear and multivalue methods
   2. Method description
   3. Interface for method description
      • Variables
        1. Example
      • Equations
        1. Example
      • Starting procedure
        1. Example
      • Implicit equation solver
        1. Example
      • Error control
        1. Example
   4. Method properties
   5. Properties automatic identification
      • Explicit/ implicit method
      • Onestep/ multistep method
      • Onestage/ multistage
      • Onederivative/ multiderivative
      • Order
      • Error constant
      • Stability domain
      • Computation time
      • Example
   6. Set of methods
      • Test methods
      • Interface facilities
      • Example
4. Solutions
   1. Generic solving procedure
   2. Selection of computing parameters
      • Non-expert
        1. Global error
        2. Maximum stepsize
        3. Initial stepsize
        4. Number of steps
        5. Computing time
        6. Variable stepsize
        7. Other informations
        8. Example
      • Expert
        1. Control parameters
        2. Method selection
        3. Example
   3. Solution representation
      • Tabular form
        1. Final values
        2. All computed values
        3. Selecting components
      • Graphical form
        1. Two-dimensional graphics
           1. Parameters
           2. Example
        2. Three-dimensional graphics
           1. Parameters
           2. Example
      • Interface facilities
        1. Example
   4. Distributed computations
      • Motivation
      • Classification
        1. Parallelism across system
        2. Parallelism across method
        3. Parallelism across time
      • Tool capabilities
        1. Parallelism across system
           1. Example
        2. Parallelism across method
           1. Example
        3. Parallelism across time
           1. Example
5. References

---