On the Integration of Stiff ODEs Using Block Backward Differentiation Formulas of Order Six
Amiratul Ashikin Nasarudin, Zarina Bibi İbrahim, Haliza Rosali
Abstract
In this research, a six-order, fully implicit Block Backward Differentiation Formula with two off-step points (BBDFO(6)), for the integration of first-order ordinary differential equations (ODEs) that exhibit stiffness, is proposed. The order, consistency and stability properties of the method are discussed, and the method is found to be zero stable and consistent. Hence, the method is convergent. The numerical comparisons with the existing methods of a similar type are given to demonstrate the accuracy of the derived method.
Topics & Concepts
OdeOrdinary differential equationBackward differentiation formulaMathematicsConsistency (knowledge bases)Block (permutation group theory)Applied mathematicsStability (learning theory)Stiff equationLinear multistep methodOrder (exchange)Type (biology)StiffnessNumerical differentiationDifferential (mechanical device)Differential equationMathematical analysisComputer scienceDifferential algebraic equationGeometryPhysicsEconomicsThermodynamicsFinanceMachine learningEcologyBiologyNumerical methods for differential equationsDifferential Equations and Numerical MethodsElectromagnetic Simulation and Numerical Methods