Sixth‐order, P‐stable, Numerov‐type methods for use at moderate accuracies
Marina A. Medvedeva, Theodore E. Simos, Ch. Tsitouras
Abstract
We consider a family of half‐implicit Numerov‐type methods for the numerical solution of the problem y ′′ = f ( x , y ) . These methods use off‐step points and waste four function evaluations (stages) per step. They attain sixth algebraic orders, while other methods of this type need five function evaluations per step. After we exploit this reduction in stages we construct a particular method and present various numerical tests on stiff periodic problems that justify its efficiency.
Topics & Concepts
MathematicsType (biology)Algebraic numberReduction (mathematics)Applied mathematicsOrder (exchange)Construct (python library)Function (biology)Mathematical analysisGeometryComputer scienceEconomicsFinanceEvolutionary biologyEcologyProgramming languageBiologyNumerical methods for differential equationsMatrix Theory and AlgorithmsDifferential Equations and Numerical Methods