id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3423	Gondal, Muhammad Asif; Rehman, Inayatur; Razzaque, Asima	Convergence of an Exponential Runge–Kutta Method for Non-smooth Initial Data	2019	16	.pdf	application/pdf	4659	323	78	− τ − tn h g(tn + h) ) dτ. (19) By using Taylor series we can write g(τ) = g(tn) + (τ − tn)g′(tn) = ∫ tn+1 tn e(tn+1−τ)ABu(τ)dτ − h(ϕ1(hA)− ϕ2(hA))Bun − hϕ2(hA)Bun2, (26) since we can write∫ tn+1 tn e(tn+1−τ)ABu(τ)dτ = ∫ tn+1 tn e(tn+1−τ)AB ( u(tn)− τ − tn h u(tn) + τ − tn h u(tn + h) + u(τ)− u(tn) + τ − tn h u(tn)− τ − tn h u(tn + h) ) dτ = hϕ1(hA)Bu(tn)− hϕ2(hA)Bu(tn) + hϕ2(hA)Bu(tn+1) + ∫ tn+1 tn e(tn+1−τ)AB ( u(τ)− u(tn) + τ − tn h u(tn) − τ − tn h u(tn + h) ) dτ. (27) Using (27) in (26) and simplifying, we have εn+1(u)	cache/ejpam-3423.pdf	txt/ejpam-3423.txt