MATLAB ODE45 and ODE15s solvers comparison study

Skills or knowledge: Knowledge of ODE45 and ODE15s solvers

Software or programs used: MATLAB programming

• MATLAB ODE45 solver:

• ODE45 solver in MATLAB is a solver for initial value ordinary differential equation problems .The ODE45 solver uses fourth order Runge –Kutta numerical method for solving the ODEs.It is an explicit solver .

• MATLAB ODE15s solver:

• ODE15s solver in MATLAB is a solver for initial value ordinary differential equation problems .The ODE15s solver uses fourth order Runge –Kutta numerical method for solving the ODEs.It is an implicit solver .

• Problem definition:

• The ODE 45 solver and ODE 15s solvers will be compared by solving a stiff ODE and a non-stiff ODE each.The solution and the internal time steps taken by the solvers will be compared.

• Result analysis:

• The internal time steps taken by the solvers to solve the ODE was analysed.

• The ODE 45 solver takes 12100 steps to compute the solution for the stiff ODE for 100 s physical time.The ODE15s solver takes only 86 time steps to cmpute the solution for the same stiff ODE for 100s physical time .

• This shows the implicit nature of the ODE15s solvers.

• Thus the ODE45 solver is explicit in nature and ODE15S solver is implicit in nature.This makes ODE15S suitable for solving stiff ODE initial value problems.