New modified shifted Chebyshev polynomials (MSCPs) have been constructed over the
interval [α, β]. These polynomials are utilized as basis functions with the application of the …

In this paper, orthonormal Bernoulli collocation method has been developed to obtain the
approximate solution of linear singular stochastic Itô‐Volterra integral equations. By …

We propose an effective method based on the reproducing kernel theory for nonlinear
Volterra integro-differential equations of fractional order. Based on the Bernoulli polynomials …

In this paper, the variable order fractional derivative in the Heydari-Hosseininia sense is
employed to define a new fractional version of 2D reaction-advection-diffusion equation. An …

This present investigation is contemplated to provide Legendre spectral collocation method
for solving multi-Pantograph delay boundary value problems (BVPs). In this regard, an …

In this work, we propose a numerical framework for solving a class of Lienard's equation.
This equation arises in the development of radio and vacuum tube technology. The spatial …

This research involves the development of the spectral collocation method based on
orthogonalized Bernoulli polynomials to the solution of time-fractional convection-diffusion …

This work develops an optimization method based on a new class of basis function, namely
the generalized Bernoulli polynomials (GBP), to solve a class of nonlinear 2-dim fractional …

A collocation method based on Bernoulli polynomial is developed to compute the
eigenvalues and eigenfunctions of some known fourth-order Sturm-Liouville problems …

In this work we present a fast and accurate numerical approach for the higher-order
boundary value problems via Bernoulli collocation method. Properties of Bernoulli …