English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper presents a direct numerical scheme to approximate the solution ofall classes of nonlinear Volterra integral equations of the first kind. Thiscomputational method is based on operational matrices and vectors. Theoperational vector for hybrid block pulse functions and Chebyshev polynomialsis constructed. The scheme transforms the integral equation to a matrixequation and solves it with a careful estimate of the error involved. The maincharacteristic of the scheme is the low cost of setting up the equationswithout using any projection method which is the consequence of usingoperational vectors. Simple structure to implement, low computational cost andperfect approximate solutions are the major points of the presented method.  Error analysis and comparisons with other existing schemes demonstrate theefficiency and the superiority of our scheme.

Direct numerical scheme for all classes of nonlinear Volterra integral equations of the first kind