Abstract
This paper is devoted to studying the boundary value method for Volterra integral equations. High order numerical schemes are devised by using special multistep collocation methods, which depend on numerical approximations of the solution in the next several steps. Stability analysis illustrates these methods enjoy wide absolutely stable regions. With the help of efficient evaluation for highly oscillatory integrals, these methods are applied to solving Volterra integral equations with highly oscillatory kernels. Both theoretical and numerical results show they share the property that the higher the oscillation, the better the accuracy of the approximations.
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Notes
In the remaining part, we will abbreviate \(F_n(t_{n,i})\) to [Lag Term] for simplicity.
To make use of the same collocation grid as CBVM, the stepsize of CCM is chosen to be 2h.
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We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
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This work is supported by No.11371376 of NSF of China, the Innovation-Driven Project and the Mathematics and Interdisciplinary Sciences Project of Central South University.
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Ma, J., Xiang, S. A Collocation Boundary Value Method for Linear Volterra Integral Equations. J Sci Comput 71, 1–20 (2017). https://doi.org/10.1007/s10915-016-0289-3
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DOI: https://doi.org/10.1007/s10915-016-0289-3