ABSTRACT

R(x, t) = It - ajxx - Qf + F (12.183) The residual R(x, t) is multiplied by a set of weighting functions Wk(x) (k = I, 2, ...) and integrated over the global physical domain D(x) to obtain the weighted residual integral, which is equated to zero. Consider the general weighting function W(x). Then,

I(f(x, t)) = J: W(1t - ajxx - Qf + F) dx = 0 (12.184) where I(f(x, t)) denotes the weighted residual integral.