Does the order of the fixed step solver has any influnce on the stability of the simulink model?

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I use fixed step solver for my models. I would like to know the influence of solver order on the stability of the model. I use ode1 and observe that some of the signals have oscillating behavior. Can I remove the oscillations by selecting a higher order fixed step solver like ode3 or ode5 etc. Thanks in advance!

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