In this paper, we compare two methods for solving Nonlinear Nonhomogeneous Volterra-Integral Equations with known exact algebraic solutions using the "Modified Decomposition Method" and demonstrate the existence and uniqueness of such solutions. Initially, using a numerical technique, a near-exact answer was quickly and easily obtained. Secondly, knowing that a solution to a multi-term Volterra equation always produces a partial combination of the input terms, a combinatory system was then used to find the correct combination representing the exact solution. This method grows exponentially and is only practical for a few terms Volterra equations. Both approaches are detailed with examples using Maple software with performance measurements that show that the numerical system is the winner if a near-exact solution is sufficient enough, which the case for most engineering applications is. For scientific and mathematical applications, the combinatory approach is preferred.
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4 December 2023
2ND INTERNATIONAL CONFERENCE OF MATHEMATICS, APPLIED SCIENCES, INFORMATION AND COMMUNICATION TECHNOLOGY
1–2 May 2022
Baghdad, Iraq
Research Article|
December 04 2023
Decomposition method with changes modified for solving nonlinear nonhomogeneous volterra integral equations
Salam Adil Majeed;
Salam Adil Majeed
a)
Mathematical Department, College of Education, University of Al-Mustansiriyah
, Baghdad, Iraq
a)Corresponding author: [email protected]
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Alan Jalal Abdulqader
Alan Jalal Abdulqader
b)
Mathematical Department, College of Education, University of Al-Mustansiriyah
, Baghdad, Iraq
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a)Corresponding author: [email protected]
AIP Conf. Proc. 2834, 080021 (2023)
Citation
Salam Adil Majeed, Alan Jalal Abdulqader; Decomposition method with changes modified for solving nonlinear nonhomogeneous volterra integral equations. AIP Conf. Proc. 4 December 2023; 2834 (1): 080021. https://doi.org/10.1063/5.0161632
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