In this research, we consider the system of linear Volterra-Fredholm integro-differential equations (SVFIDEs). The main aim of this research is to approximate the integral by Gauss-Kronrod-Legendre quadrature rules and then using quintic B-spline as the bases function. The unknown coefficients in combination determine by collocation method. The arising system of algebraic linear can be solved via iterative method. Error analysis is investigated theoretically. Numerical text problems are considered to justify the applicability and efficient nature of our approach, comparison of the results justify the considerable accuracy and efficiency proposed methods. The extended parameter in valued in the spline can be chosen in such a way to improve the accuracy also.
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Mahmoodi, Z. (2026). The Solution for Systems of High-Order Linear Volterra-Fredholm Integro-Differential Equations. Analytical and Numerical Solutions for Nonlinear Equations, 11(1), 93-100. doi: 10.22128/ansne.2026.3231.1190
MLA
Zahra Mahmoodi. "The Solution for Systems of High-Order Linear Volterra-Fredholm Integro-Differential Equations", Analytical and Numerical Solutions for Nonlinear Equations, 11, 1, 2026, 93-100. doi: 10.22128/ansne.2026.3231.1190
HARVARD
Mahmoodi, Z. (2026). 'The Solution for Systems of High-Order Linear Volterra-Fredholm Integro-Differential Equations', Analytical and Numerical Solutions for Nonlinear Equations, 11(1), pp. 93-100. doi: 10.22128/ansne.2026.3231.1190
VANCOUVER
Mahmoodi, Z. The Solution for Systems of High-Order Linear Volterra-Fredholm Integro-Differential Equations. Analytical and Numerical Solutions for Nonlinear Equations, 2026; 11(1): 93-100. doi: 10.22128/ansne.2026.3231.1190
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