Problems: 6.1, 6.5, 6.6

I am stuck on these and need help to figure them out

thank you

61 What is the grid spacing Ar if you discretize the space-re [-1, 1 ] with 51 nodes? 6.2 What is the equation for ci for the solution of the diffusion equation d2cdr2-0 with a no-flux boundary condition at the left boundary? 6.3 In a one-dimensional boundary value problem with a no-flux condition on the left boundary, what is the relationship between the fictitious node and the nodes in the domain? 64 Consider a coupled system of boundary value problems for x and y. If the unknowns are in a vector z in an order that preserves the band structure, what are the first five entries in z? 6.5 Consider the differential equation d'y dx2 subject to(0) = 0 and y(1) = 1 If this equation is solved using centered finite differences and three nodes, what is the value of interor node, y2? 6.6 Use Taylor series expansions to derive the centered finite difference formula for the third derivative, = de