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 Original Message (ID '347830') By Bill Simpson: If you evaluate With[{s = 0.1, h = 0.5, r0 = 0.01, r1 = 1}, odes2 = {...YourOdes2CodeUnChanged...} ] and inspect the output very very very carefully, using Zoom may help, you will see of examples of 0. YT0A[t] and similar constructs. That is saying this function is being multiplied by "approximately zero" or floating point zero. Those "worry me." If you then kill your kernel and restart evaluation of With[{s = 1/10, h = 1/2, r0 = 1/100, r1 = 1}, odes2 = {...YourOdes2CodeWithALLDecimalsReplacedByExactFractions...} ] then the result is a little smaller, all decimal points have disappeared and the functions being multiplied by "approximately zero" are gone. If you can duplicate that then try this next. In[3]:= solnApproximate=NDSolve[odes2,{YT0A[t],YT0a[t],YT1A[t],MTA[t]},{t,0,100}] Out[3]= {{ YT0A[t]->InterpolatingFunction[{{0.,100.}},<>][t], YT0a[t]->InterpolatingFunction[{{0.,100.}},<>][t], YT1A[t]->InterpolatingFunction[{{0.,100.}},<>][t], MTA[t]->InterpolatingFunction[{{0.,100.}},<>][t]}} In[4]:= Plot[YT0A[t]/.solnApproximate,{t,0,100}] Out[4]= ...NiceIncreasingPlotSnipped... In[5]:= Plot[YT0a[t]/.solnApproximate,{t,0,100}] Out[5]= ...NiceDecreasingPlotSnipped... In[6]:= Plot[YT1A[t]/.solnApproximate,{t,0,100}] Out[6]= ...NiceIncreasingPlotSnipped... In[7]:= Plot[MTA[t]/.solnApproximate,{t,0,100}] Out[7]= ..NiceIncreasingPlotSnipped... This worries me a little less now. If you can duplicate all this and verify that the plots make sense for your problem then perhaps we can think what the next step might be. There is a great line in a 25 year old book by Donald Norman, called I believe "The Psychology of Everyday Things", something like "If you had 1/10 the trouble with a toaster that you have with a computer you would kick it down the stairs..." and now toasters have computers in them. I apologize for your frustration, it isn't even my fault, but I still apologize.