Search results for "Taylor method"

showing 3 items of 3 documents

Approximate Taylor methods for ODEs

2017

Abstract A new method for the numerical solution of ODEs is presented. This approach is based on an approximate formulation of the Taylor methods that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their derivatives, are needed, just as in classical Runge–Kutta schemes. Compared to Runge–Kutta methods, the number of function evaluations to achieve a given order is higher, however with the present procedure it is much easier to produce arbitrary high-order schemes, which may be important in some applications. In many cases the new approach leads to an asymptotically lower computational cost when compared to the Taylor expansio…

di Bruno's formulaODE integratorsGeneral Computer ScienceTaylor methodsComputer Science (all)MathematicsofComputing_NUMERICALANALYSISGeneral EngineeringOde010103 numerical & computational mathematicsFunction (mathematics)Present procedure01 natural sciencesFaà di Bruno's formula; ODE integrators; Taylor methods; Computer Science (all); Engineering (all)010101 applied mathematicssymbols.namesakeEngineering (all)FaÃ&nbspTaylor seriessymbolsCalculusApplied mathematics0101 mathematicsMathematics
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Reprint of: Approximate Taylor methods for ODEs

2018

Abstract A new method for the numerical solution of ODEs is presented. This approach is based on an approximate formulation of the Taylor methods that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their derivatives, are needed, just as in classical Runge–Kutta schemes. Compared to Runge–Kutta methods, the number of function evaluations to achieve a given order is higher, however with the present procedure it is much easier to produce arbitrary high-order schemes, which may be important in some applications. In many cases the new approach leads to an asymptotically lower computational cost when compared to the Taylor expansio…

ODE integratorsGeneral Computer ScienceTaylor methodsMathematicsofComputing_NUMERICALANALYSISGeneral EngineeringOdeFunction (mathematics)Present procedure01 natural sciences010101 applied mathematicsFaà di Bruno's formulasymbols.namesakeTaylor seriessymbolsApplied mathematicsOrder (group theory)0101 mathematicsMathematicsComputers & Fluids
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Stiffness-Adaptive Taylor method for the integration of non-stiff and stiff kinetic models

1992

A systematic derivation procedure that greatly facilitates the application of the Taylor method to the integration of kinetic models is developed. In addition, an algorithm that gives the integration step as a function of the required level of accuracy is proposed. Using the Taylor method, application of this algorithm is immediate and largely reduces the integration time. In addition, a new method of integration of kinetic models, whose most important feature is the self-adaptability to the stiffness of the system along the integration process, is developed. This “stiffness-adaptive” Taylor method (SAT method) makes use of several algorithms, combining them to meet the particular requireme…

Time delay and integrationProcess (engineering)MathematicsofComputing_NUMERICALANALYSISStiffnessGeneral ChemistryFunction (mathematics)Kinetic energyDerivation procedureComputational MathematicsTaylor methodFeature (computer vision)medicinemedicine.symptomAlgorithmMathematicsJournal of Computational Chemistry
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