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Finite difference schemes for differential equations

Finite difference schemes for differential equations

(1) ~~~~~L = d p(x) d + q(x) and the related variational problem for the functional b ~~~~~~~~~~b (2) Q(u) = ] (pu'2 + qu') dx - 2 fu dx viz., min Q(u) uE Q where the class Q consists of smooth functions u(x) satisfying u(a) = u(b) = 0. …