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Backward induction is the process of reasoning backwards in time from the end of a problem or situation to determine a sequence of optimal actions. It proceeds by examining the last point at which a decision is to be made and then identifying what action would be most optimal at that moment.

The backward Euler method is an implicit method: the new approximation + appears on both sides of the equation and thus the method needs to solve an algebraic equation for the unknown +. For non- stiff problems this can be done with fixed-point iteration :

List of algorithms – Wikipedia

List of algorithms – Wikipedia

Dynamic programming – Wikipedia

Forward–backward algorithm – Wikipedia

The forward– backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions ::= … i.e. it computes for all hidden state variables ∈ { … } the distribution ( | :).This inference task is usually called smoothing.The algorithm makes use of the principle of dynamic …

The backward differentiation formula (BDF) is a family of implicit methods for the numerical integration of ordinary differential equations.They are linear multistep methods that for a given function and time approximate the derivative of that function using information from already computed time points thereby increasing the accuracy of the approximation.

The Euler method is + = + ( ). so first we must compute ( ).In this simple differential equation the function is defined by ( ) =.We have ( ) = ( ) =By doing the above step we have found the slope of the line that is tangent to the solution curve at the point ( ).Recall that the slope is defined as the c…