Numerical solutions of time-fractional Klein-Gordon equations by clique polynomials
R.M. Ganji, Hossein Jafari, Maluti Kgarose, Ardeshir Karami Mohammadi
Abstract
This work adopts to the time-fractional Klein–Gordon equation (FKGE) in the Caputo sense. We present a new technique using the clique polynomial as basis function for the operational matrices to obtain solution of time-FKGE. The key advantage of this technique is converting the time-FKGE to algebraic equations, which can be simply solved the problem under study. For the approximation of a bivariate function using the clique polynomial, an error bound is given. Numerical results derived using the proposed technique are compared with the exact solution. The results show that the proposed technique is very user friendly for solving the time-FKGE and accurate.
Topics & Concepts
CliqueMathematicsBivariate analysisPolynomialApplied mathematicsFunction (biology)Algebraic equationAlgebraic numberClique problemKey (lock)Mathematical analysisDiscrete mathematicsCombinatoricsComputer scienceChordal graphPhysicsGraphBiologyStatisticsComputer securityQuantum mechanics1-planar graphEvolutionary biologyNonlinear systemFractional Differential Equations SolutionsNonlinear Waves and SolitonsNumerical methods for differential equations