Swarm Intelligence for Solving Some Nonlinear Differential Equations

The Euler method is a well-known numerical technique employed for solving initial value problems of ordinary differential equations. solution obtained through Euler's subject to significant inaccuracies, which tend amplify with each successive iteration. Particle Swarm Optimization (PSO) algorithm highly effective finding optimal solutions both linear and nonlinear optimization problems. In this particular investigation, the PSO was utilized solve associated method, on other hand, employs equidistant grid points approximate solutions, can result in errors substantial deviation from actual solution. reliable approach achieving problems, including contrast, uses evenly spaced estimate lead inaccuracies true To address issue, new developed using determine non-uniform that minimize approximation. Increasing number enhances accuracy reduces errors. Numerical calculations were performed compare traditional formulae, demonstrating its superiority overcoming existing limitations delivering numerous benefits.