scholarly journals A weak solution theory for stochastic Volterra equations of convolution type

2021 ◽  
Vol 31 (6) ◽  
Author(s):  
Eduardo Abi Jaber ◽  
Christa Cuchiero ◽  
Martin Larsson ◽  
Sergio Pulido
Keyword(s):  
Weak Solution ◽  
Convolution Type ◽  
Volterra Equations ◽  
Solution Theory ◽  
Weak Solution Theory

scholarly journals A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

2021 ◽  
Vol 47 (3) ◽  
Author(s):  
Timon S. Gutleb
Keyword(s):  
Open Source ◽  
Spectral Method ◽  
Jacobi Polynomial ◽  
Numerical Experiments ◽  
Exponential Convergence ◽  
Analytic Solutions ◽  
Convolution Type ◽  
Volterra Equations ◽  
Polynomial Bases ◽  
Sparsity Structure

AbstractWe present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods.

scholarly journals Numerical Solutions to Fractional Perturbed Volterra Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
B. Bandrowski ◽  
A. Karczewska ◽  
P. Rozmej
Keyword(s):  
Wave Equations ◽  
Numerical Solutions ◽  
Kernel Functions ◽  
Convolution Type ◽  
Volterra Equations

In the paper, a class of perturbed Volterra equations of convolution type with three kernel functions is considered. The kernel functions , , , correspond to the class of equations interpolating heat and wave equations. The results obtained generalize our previous results from 2010.

scholarly journals A Series Approach to Perturbed Stochastic Volterra Equations of Convolution Type

2015 ◽  
Vol 05 (11) ◽  
pp. 660-671
Author(s):  
Anna Karczewska ◽  
Bartosz Bandrowski
Keyword(s):  
Convolution Type ◽  
Volterra Equations
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