TY - JOUR
ID - 10520
TI - On the numerical approximation of Volterra integro-differential equation using Laplace transform
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Uddin, Marjan
AU - Uddin, Musafir
AD - Department of basic sciences and islamiat, University of engineering and technology Peshawar, pakistan
Y1 - 2020
PY - 2020
VL - 8
IS - 2
SP - 305
EP - 313
KW - Volterra Integro-differential equation(VIDE)
KW - Hyperbolic and parabolic contours
KW - Laplace Transforms
KW - Trapezoidal rule
DO - 10.22034/cmde.2020.27877.1378
N2 - In this work we constructed a numerical scheme to approximate the Volterra integro- differential equations of convolution type using Laplace transform. The solution of the problem is recovered using inverse Laplace transform as contour integral in the complex plane. The integral is then approximated along a suitable contour using the trapezoidal rule with equal step size. The solution accuracy depends on optimal contour of integrations to compute accurately the inverse Laplace transform. For better accuracy two types of contour parabolic and hyperbolic are used which are available in the literature. The performance of the numerical scheme is tested for different examples. The actual error well agree with the corresponding error estimates of the proposed numerical scheme for both parabolic as well as hyperbolic contours.
UR - https://cmde.tabrizu.ac.ir/article_10520.html
L1 - https://cmde.tabrizu.ac.ir/article_10520_8b7cec7ef658ab0d5da6005d7784f82f.pdf
ER -