1. Consider the differential equation dy dt -10y; y(0) = 1. = -- (a) Obtain...
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1. Consider the differential equation dy dt -10y; y(0) = 1. = -- (a) Obtain a finite difference approximation for the above equation using Forward Differencing approach. Your approximation should be general, providing an equation for Yn+1 using the solution Yn, where Yn+1 and Yn represent solutions at tnt1 and tn. Use At = tnt1 - tn. (b) Using linear stability analysis, find any constraints on the time-step (At) to obtain a stable so- lution. Then identify if the forward differencing method is conditionally stable, unconditionally unstable, or unconditionally stable for the above
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