1) a) (15 points) Second order accurate Runge-Kutta Method (RK2) is given below: y(x+h) = y(x) +w,F,+w₂F₂ where F₁ = hf (x, y) F₂ = hf (x + ah, y + BF₁) Derive the weights W₁, W2 and coefficients a and ß for RK2. Hint: Show that the error using RK2 is the same as in second order Taylor's method. b) (10 points) Explain the following terms briefly (and give examples where appropriate): Metrics: Staggered grid Lax's equivalence theorem . Continuum assumption