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Keywords Availability and cost function Error analysis G'/G-expansion method Haar wavelets Homotopy Perturbation Method Kupershmidt equation. Laplace transform Linear Fredholm equations Singular perturbation problem, Numerical integration, Trapezoidal formula, boundary layer. Steady-state behaviour Strongly Multiplicative ,Supersubdivision,Arbitrary Supersubdivision Supplementary variables Traveling wave solutions computationally attractive generalized $F$-Minty's lemma generalized differential dominated VIP of order $\lambda$ generalized differential vector CP of order $\lambda$. half-sweep iteration linear systems, preconditioner, convergence, M-matrix, AOR iterative method. one-dimensional reaction-diffusion equation quadrature