(a) Given the following Butcher tableau: 0 1 1 NI 2 write out the equations for &i, and Yk+1 for the corresponding RK method. Then use it to compute an approximate value for y(0.2), using h = 0.1, given that y satisfies the following initial value problem: (10 marks] y(a)? 2+2 y(0) = 2 (b) Given the linear multi-step method (LMM): (8 marks] Yk+2 = 4x+1+ hlbofys) + b1f (**+1,9x+1),b2f(3x+2yx+2) find equations for by and b, in terms of by such that the method is order p=2. (a) Given the following Butcher tableau: 0 1 1 NI 2 write out the equations for &i, and Yk+1 for the corresponding RK method. Then use it to compute an approximate value for y(0.2), using h = 0.1, given that y satisfies the following initial value problem: (10 marks] y(a)? 2+2 y(0) = 2 (b) Given the linear multi-step method (LMM): (8 marks] Yk+2 = 4x+1+ hlbofys) + b1f (**+1,9x+1),b2f(3x+2yx+2) find equations for by and b, in terms of by such that the method is order p=2