scholarly journals Integral Equations & Model Reduction For Fast Computation of Nonlinear Periodic Response

2021 ◽  
Author(s):  
Gergely Buza ◽  
George Haller ◽  
Shobhit Jain
Keyword(s):  
Model Reduction ◽  
Integral Equations ◽  
Fast Computation ◽  
Periodic Response

scholarly journals Hermite-Type Collocation Methods to Solve Volterra Integral Equations with Highly Oscillatory Bessel Kernels

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 168 ◽  
Author(s):  
Chunhua Fang ◽  
Guo He ◽  
Shuhuang Xiang
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Bessel Functions ◽  
Hermite Interpolation ◽  
Volterra Integral Equations ◽  
Collocation Methods ◽  
Fast Computation ◽  
Highly Oscillatory ◽  
Linear Volterra Integral Equations ◽  
Highly Oscillatory Integrals

In this paper, we present two kinds of Hermite-type collocation methods for linear Volterra integral equations of the second kind with highly oscillatory Bessel kernels. One method is direct Hermite collocation method, which used direct two-points Hermite interpolation in the whole interval. The other one is piecewise Hermite collocation method, which used a two-points Hermite interpolation in each subinterval. These two methods can calculate the approximate value of function value and derivative value simultaneously. Both methods are constructed easily and implemented well by the fast computation of highly oscillatory integrals involving Bessel functions. Under some conditions, the asymptotic convergence order with respect to oscillatory factor of these two methods are established, which are higher than the existing results. Some numerical experiments are included to show efficiency of these two methods.

SOLUTION TO THE MODEL PROBLEM OF EXCITATION OF LOADED CONIC SLOT ANTENNA BY METHOD OF SINGULAR INTEGRAL EQUATIONS

2016 ◽  
Vol 75 (20) ◽  
pp. 1799-1812
Author(s):  
V. A. Doroshenko ◽  
S.N. Ievleva ◽  
N.P. Klimova ◽  
A. S. Nechiporenko ◽  
A. A. Strelnitsky
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Model Problem ◽  
Singular Integral Equations ◽  
Slot Antenna
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