on accuracy of numerical-analytical solutionexpression for hyperchaotic r¨ossler system

Analytical solution for hyperchaotic systems have attracted increasing interestin recent years. in this paper, numerical-analytical solution for hyperchaotic r¨osslersystem is obtained via multistage homotopy analysis method (msham). an analyticalform of the solution within each time interval is given, which is not possible usingstandard numerical methods. the numerical results obtained by the msham and theclassical fourth-order runge-kutta (rk4) method are in complete agreement. moreoverthe residual error for msham solution is defined and calculated. the obtained residualerror gives accuracy with 14 digits.