Numerical study of third-order ordinary differential equations using a new class of two derivative Runge-Kutta type methods
K.C. Lee, Norazak Senu, Ali Ahmadian, Siti Nur Iqmal Ibrahim, Dumitru Bǎleanu
Abstract
This study introduces new special two-derivative Runge-Kutta type (STDRKT) methods involving the fourth derivative of the solution for solving third-order ordinary differential equations. In this regards, rooted tree theory and the corresponding B-series theory is proposed to derive order conditions for STDRKT methods. Besides, explicit two-stages fifth order and three-stages sixth order STDRKT methods are derived and stability,consistency and convergence of STDRKT methods are analysed in details. Accuracy and effectiveness of the proposed techniques are validated by a number of various test problems and compared to existing methods in the literature.
Topics & Concepts
Runge–Kutta methodsMathematicsLinear multistep methodDerivative (finance)Ordinary differential equationThird orderApplied mathematicsConvergence (economics)Consistency (knowledge bases)Numerical methods for ordinary differential equationsType (biology)Class (philosophy)Order (exchange)Stability (learning theory)Differential equationMathematical analysisDifferential algebraic equationComputer scienceGeometryEconomicsTheologyArtificial intelligencePhilosophyMachine learningFinancial economicsEconomic growthFinanceEcologyBiologyNumerical methods for differential equationsIterative Methods for Nonlinear EquationsDifferential Equations and Numerical Methods