# HOMOTOPY PERTURBATION SUMUDU TRANSFORM METHOD FOR ONE-TWO-THREE DIMENSIONAL INITIAL VALUE PROBLEMS

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We study some well-posedness issues of the initial value problem associated with the equation ut + uxxx + Î·Lu + uux = 0, x âˆˆ â„, t â‰¥ 0, where Î· > 0, ...(Î¾) = -Î¦(Î¾)Ã»(Î¾) and Î¦ âˆˆ â„ is bounded above. Using the theory developed by Bourgain and Kenig,...

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We introduce a matrix form of differential transformation method (DTM) and apply for nonlinear second-order initial value problems (IVPs) and boundary value problems (BVPs) of matrix models which are given by u'' (t) = f(t,u(t),u'(t)) and subject to initial conditions u(a) =u0,u'(a) = u1 and...