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Numerical solutions of nonlinear 3‐dimensional Volterra integral‐differential equations with 3D‐block‐pulse functions
Author(s) -
Manafian Jalil,
Bolghar Peyman
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4936
Subject(s) - mathematics , volterra integral equation , nonlinear system , uniqueness , block (permutation group theory) , pulse (music) , differential equation , integral equation , mathematical analysis , computer science , geometry , telecommunications , physics , quantum mechanics , detector
This paper studies nonlinear 3‐dimensional Volterra integral‐differential equations, by implementing 3‐dimensional block‐pulse functions. First, we prove a theorem and corollary about sufficient condition for the minimum of mean square error under the block pulse coefficients and uniqueness of solution of the nonlinear Volterra integral‐differential equations. Then, we convert the main problem to a nonlinear system to the 3‐dimensional block‐pulse functions. In addition, illustrative examples are included to demonstrate the validity and applicability of the presented method.