(4c) Assume equidistant meshes and reconstruction of slopes by a particular av- eraging. More precisely, the...

 

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(4c) Assume equidistant meshes and reconstruction of slopes by a particular av- eraging. More precisely, the M-piecewise cubic function s is to satisfy the generalized interpolation conditions s(xj) = f(xj), s'(xj) = (f(x2)+4(21)-3f(x0) f(xj+1)-f(xj-1) 2h for j = 0, 2h for j = 1,...,n-1, for j = n. | 3f(x)-4f(n-1)+f(In-2) 2h What will be the rate of h-convergence of this scheme (in sup-norm)? (You can solve this exercise either theoretically or determine an empiric convergence rate in a numerical experiment.) HINT: If you opt for the theoretical approach, you can use what you have found in sub- subsection (4a). To find perturbation bounds, rely on the Taylor expansion formula with remainder, see [1, Ex. 1.5.60]. (4c) Assume equidistant meshes and reconstruction of slopes by a particular av- eraging. More precisely, the M-piecewise cubic function s is to satisfy the generalized interpolation conditions s(xj) = f(xj), s'(xj) = (f(x2)+4(21)-3f(x0) f(xj+1)-f(xj-1) 2h for j = 0, 2h for j = 1,...,n-1, for j = n. | 3f(x)-4f(n-1)+f(In-2) 2h What will be the rate of h-convergence of this scheme (in sup-norm)? (You can solve this exercise either theoretically or determine an empiric convergence rate in a numerical experiment.) HINT: If you opt for the theoretical approach, you can use what you have found in sub- subsection (4a). To find perturbation bounds, rely on the Taylor expansion formula with remainder, see [1, Ex. 1.5.60].

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To find the rate of hconvergence of this scheme lets first consider the theoretical approach by ... View the full answer