Grid-Based and Hybrid Five-Step Block Runge-Kutta Methods for Solving Linear and Nonlinear First-Order Ordinary Differential Equations

Key Points

• The hybrid block Runge Kutta method converges faster for both linear and nonlinear equations, enhancing solution accuracy.
• Testing two problems demonstrated the effectiveness of the 5th step hybrid block Runge Kutta method in solving ordinary differential equations.
• Hybrid methods utilize interpolation and collocation approaches, integrating multiple strategies for more efficient computations.
• These grid-based methods have potential applications in various fields requiring the solution of first-order ordinary differential equations.