Numerical and theoretical analysis of the parabolic partial differential equation through the Bernoulli wavelet collocation scheme

We present a novel scheme called the Bernoulli wavelet collocation scheme for the parabolic partial differential equations (PDEs) with different boundary circumstances. We utilized the linear combination of the basis concept to develop the functional integration matrix. Next, we employed these matrices to create a Bernoulli wavelet collocation scheme. By applying collocation points, we can transform parabolic PDEs into a set of algebraic equations, which can be solved by the Newton–Raphson technique to obtain an approximate solution. In this article, we solved five problems to justify the current approach. The obtained outcome is expressed through the graphs and tables. Also, these outcomes are compared with results available in the literature. The recommended technique is testified for convergence in terms of theorems.