Abstract We analyze the nonlinear (2+ 1)-dimensional KdV–mKdV equation with Caputo
fractal–fractional operator. Some theoretical features are demonstrated via fixed point …

This study presents a novel class of multi-derivative integrating techniques designed to
effectively address singular initial value problems. This study not only delves into the …

This work aims to implement a one-step block method with three optimized hybrid points for
solving singularly perturbed nonlinear initial value problems on non-uniform meshes. The …

A one-step three-parameter optimized hybrid block method and second derivative hybrid
block method with optimized points were proposed to solve first-order ordinary differential …

Using a carefully selected step and off-step points produced from the Bhaskara Cosine
approximation formula and Gauss-Lobato grid points with constant step size, this numerical …

Perturbed basis of a hybrid block method is a modification of the original basis functions,
designed to improve the performance of the method when differential equations posses …

Conventionally, the method of solving fourth order initial value problems of ordinary
differential is to first reduce it to a system of first order differential equation. This approach …

A seventh order second derivative method with optimized hybrid points is proposed for the
solution of first-order ordinary differential equations. The techniques of interpolation and …

This paper proposes a 4-step block method for the numerical solution of first to fifth orders of
ordinary differential equations (ODEs). The coefficients of the proposed scheme are …