Matlab ODE solver and Convergence question

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Hi all

I am using the ode45, ode113, ode23t (for "stiff" and "nonstiff" problems)... ode Matlab solvers for a system of ODEs. My question has to do with the convergence and the control of the error. Is convergence always guaranteed using these solvers ? Is there a way to check this ?

The only feedback that i m getting from Matlab is the adjustment of the "Relative and Absolute" Tolerances. For example, if Abstol it is too low, Matlab will notify AbsTol was increased to a specific value. However, i never get any errors/messages and everything "looks" to be fine (even though the solution looks weird) - i never know if the solution has converged.

ps I use low tolerances (1e-08 or smaller) for both AbsTol, RelTol.Thanks in advance

 

[NateD]

for the helpYes, convergence is usually guaranteed using these solvers. You can check it by looking at the error estimates given by the solver. These estimates come from the local truncation error and should decrease as the step size decreases. If the errors are not decreasing, then you may want to look for a different numerical method.

 

[oswaler]

for any help or insights.

I can say that convergence is not always guaranteed when using ODE solvers, including those in Matlab. While these solvers are designed to provide accurate solutions, there are certain factors that can affect their convergence, such as the stiffness of the problem and the chosen tolerances.

To check for convergence, it is important to monitor the error in the solution as the solver progresses. This can be done by setting the 'OutputFcn' property in the solver options to a function that calculates and displays the error. This will help you determine if the solution is converging or not.

Additionally, it is important to carefully choose the tolerances for your problem. Setting them too low can result in the solver taking longer to converge, while setting them too high can result in less accurate solutions. It is recommended to start with higher tolerances and gradually decrease them until a satisfactory solution is obtained.

In conclusion, while ODE solvers can provide accurate solutions, it is important to carefully monitor the convergence and choose appropriate tolerances for your specific problem. It is also helpful to consult with other experts or resources for further insights and troubleshooting.