Numerical Analysis Final Exam Review
Accuracy - ANS-how closely a computed or measured value agrees with the true
value.
Precision - ANS-how closely individual computed or measured values agree with
each other.
Total Absolute error, Et - ANS-|Et| = y_actual - y_approx
Total relative error, εt - ANS-εt = ((y_actual - y_approx)/y_actual)*100%
Approximate relative error, εa - ANS-(present approximation - previous
approximation)/present approximation
Machine epsilon - ANS-The smallest positive number that the computer can store.
Stability/unstable solution - ANS-Every numerical method for IVP's suffers from the
problem of stability. A numerical solution for an IVP is unstable if the error for the
approximation grows exponentially even though the actual solution is bounded.
Initial value problem - ANS-A differential equation, usually involving time, that
comes with an initial value, y(t_0) = y_0.
Local truncation error - ANS-Truncation without global propagation error during a
single iteration.
Propagation error - ANS-The error associated with how much a numerical
approximation differs from the actual graph after each iteration.
Boundary value problem - ANS-A differential equation, usually involving spatial
dimensions, that comes with multiple boundary values, y(x_0) = y_0. and y(x_1) =
y_1.
Dirichlet boundary condition - ANS-Specifies a value for the function on the
boundary, T(L) = T_0.
Neumann boundary condition - ANS-Specifies a value for the derivative of the
function on the boundary, T'(L) = 6.
Robin boundary condition - ANS-Combines the Dirichlet and Neumann boundary
conditions, 3T(L) - 4T'(L) = 8.
Bisection method - ANS-Idea: Start with an interval with a root with a sign change,
split the interval in half, test for sign change from x_min to x_bar. If there is a sign
Accuracy - ANS-how closely a computed or measured value agrees with the true
value.
Precision - ANS-how closely individual computed or measured values agree with
each other.
Total Absolute error, Et - ANS-|Et| = y_actual - y_approx
Total relative error, εt - ANS-εt = ((y_actual - y_approx)/y_actual)*100%
Approximate relative error, εa - ANS-(present approximation - previous
approximation)/present approximation
Machine epsilon - ANS-The smallest positive number that the computer can store.
Stability/unstable solution - ANS-Every numerical method for IVP's suffers from the
problem of stability. A numerical solution for an IVP is unstable if the error for the
approximation grows exponentially even though the actual solution is bounded.
Initial value problem - ANS-A differential equation, usually involving time, that
comes with an initial value, y(t_0) = y_0.
Local truncation error - ANS-Truncation without global propagation error during a
single iteration.
Propagation error - ANS-The error associated with how much a numerical
approximation differs from the actual graph after each iteration.
Boundary value problem - ANS-A differential equation, usually involving spatial
dimensions, that comes with multiple boundary values, y(x_0) = y_0. and y(x_1) =
y_1.
Dirichlet boundary condition - ANS-Specifies a value for the function on the
boundary, T(L) = T_0.
Neumann boundary condition - ANS-Specifies a value for the derivative of the
function on the boundary, T'(L) = 6.
Robin boundary condition - ANS-Combines the Dirichlet and Neumann boundary
conditions, 3T(L) - 4T'(L) = 8.
Bisection method - ANS-Idea: Start with an interval with a root with a sign change,
split the interval in half, test for sign change from x_min to x_bar. If there is a sign
