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The study aims to develop a numerical method for solving third-order initial value problems using an optimized hybrid Volterra integral equation.

March 30, 2026Open Access

Development and Implementation of a Numerical method to Solve Third-Order Initial Value Problems Using an Optimized Hybrid Volterra Integral Equation of the Second Kind

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Numerical technique addresses third-order initial value problems, indicating improved convergence and stability.

The study aims to develop a numerical method for solving third-order initial value problems using an optimized hybrid Volterra integral equation.
Developed a two-step optimized hybrid numerical approach
Utilized power series and exponential fitting as basis functions
Focused on addressing stiff initial value problems
Demonstrated through numerical examples
Exhibited enhanced convergence characteristics
Showed increased precision and reduced computing expense
Demonstrated superior stability compared to conventional methods

Benard et al. (2026) studied this question.

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