Derivation of explicit 6(4) pair of hybrid methods for special second order ordinary differential equations

Samat, Faieza; Razak, Nor Farhah

doi:10.1063/1.5041608

Cited by 1 publication

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consider a class of three-stage explicit hybrid method represented by Table 2: The fourth-order method has the same c and A values as the sixth-order method with constant coefficients described in Section 3.1. Using the order conditions for a fourth-order explicit hybrid method as listed in [13], we obtain b 1 = 0, b 2 = 19 27 , b 3 = 4 27 and b 4 = b 3 [14]. Assume that b i are functions of θ.…”

Section: Exponentially Fitted Fourth-order Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Variable Step Exponentially Fitted Explicit Sixth-Order Hybrid Method with Four Stages for Spring-Mass and Other Oscillatory Problems

Samat

Ismail

2020

Symmetry

Self Cite

View full text Add to dashboard Cite

For the numerical integration of differential equations with oscillatory solutions an exponentially fitted explicit sixth-order hybrid method with four stages is presented. This method is implemented using variable step-size while its derivation is accomplished by imposing each stage of the formula to integrate exactly { 1 , t , t 2 , … , t k , exp ( ± μ t ) } where the frequency μ is imaginary. The local error that is employed in the step-size selection procedure is approximated using an exponentially fitted explicit fourth-order hybrid method. Numerical comparisons of the new and existing hybrid methods for the spring-mass and other oscillatory problems are tabulated and discussed. The results show that the variable step exponentially fitted explicit sixth-order hybrid method outperforms the existing hybrid methods with variable coefficients for solving several problems with oscillatory solutions.

show abstract

Section: Exponentially Fitted Fourth-order Methodsmentioning

confidence: 99%

“…The interval of absolute stability is (0, 4.42) while the error constant E = 2.08 × 10 −3[14]. Using these coefficients, the characteristic polynomial (Equation(4)) is a Schur polynomial if H < 4.42.…”

mentioning

confidence: 99%