Application of Lagrange Interpolation Method to Solve First-Order Differential Equation Using Newton Interpolation Approach

Ibrahim, Salisu (2023) Application of Lagrange Interpolation Method to Solve First-Order Differential Equation Using Newton Interpolation Approach. Eurasian Journal of Science and Engineering, 9 (1).

Text (Research Article) Application-of-Lagrange-Interpolation-Method-to-Solve-First-Order-Differential-Equation-Using-Newton-Interpolation-Approach.pdf - Published Version Download (859kB)

Abstract

One of the important problems in mathematics is finding the analytic solution and numerical solution of the differential equation using various methods and techniques. Most of the researchers tackled different numerical approaches to solve ordinary differential equations. These methods such as the Runge Kutta method, Euler’s method, and Taylor’s polynomial method have so many issues like difficulties in finding the solution that can lead to singularities or no solution. In this work, we considered Newton’s interpolation and Lagrange’s interpolation polynomial method (LIPM). These studies combine both Newton’s interpolation method and Lagrange method (NIPM) to solve first-order differential equations. The results obtained provide minimum approximative error. The result is supported by solving an example.

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