Implicit Runge-Kutta methods for second kind Volterra integral equations
1974
Implicit Runge-Kutta methods for ordinary differential equations which arise from interpolatory quadrature formulae are generalized to Volterra integral equations of the second kind. Two classes of methods are considered and shown to be convergent and numerically stable. In addition, for various choices of quadrature formulae the methods areA-stable and stifflyA-stable.
Keywords:
- Mathematical optimization
- Numerical integration
- Collocation method
- Backward differentiation formula
- Mathematical analysis
- Explicit and implicit methods
- Numerical methods for ordinary differential equations
- Integral equation
- Volterra integral equation
- Runge–Kutta methods
- Mathematics
- Gauss–Kronrod quadrature formula
- Correction
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