id author title date pages extension mime words sentence flesch summary cache txt american_scientific_journal-3507 Ampomah, Ernest Kwame; Ayensu, Akwasi; Amisigo, Barnabas; Agbenorku, Obed Comparative Analysis of Laplace Transform and Finite Difference Modeling and Simulation of Solute Transport in Soil. (Case Study: Nitrate Solute Transport in Homogeneous Soil) 2017 15 .pdf application/pdf 4881 205 57 [13] 𝐿𝐿{𝑓𝑓(𝑑𝑑)} = ∫ 𝑓𝑓(𝑑𝑑)π‘’π‘’βˆ’π‘ π‘ π‘ π‘ π‘‘π‘‘π‘‘π‘‘ = 𝐹𝐹(𝑠𝑠)∞ 0 …….………………………………………...……………………... (2.15) 𝐿𝐿{𝑓𝑓′(𝑑𝑑)} = 𝑠𝑠𝐹𝐹(𝑠𝑠) βˆ’ 𝑓𝑓(0)…………...……………………………………………………………….… (2.16) 𝐿𝐿 οΏ½πœ•πœ•πœ•πœ• πœ•πœ•π‘ π‘  οΏ½ = 𝑠𝑠𝑐𝑐̅ βˆ’ 𝑐𝑐(𝑧𝑧, 0)………….…………………………………………………..........................................(2.17) Applying the initial condition, equation (2.17) becomes: 𝐿𝐿 οΏ½πœ•πœ•πœ•πœ• πœ•πœ•π‘ π‘  οΏ½ = 𝑠𝑠𝑐𝑐̅ βˆ’ 𝑐𝑐(𝑧𝑧, 0)……………………………………………………………………………………... (2.18) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 1, pp 235-249 242 𝐿𝐿 �𝑣𝑣 πœ•πœ•πœ•πœ• πœ•πœ•πœ•πœ• οΏ½ = 𝑣𝑣 ∫ πœ•πœ•πœ•πœ• πœ•πœ•πœ•πœ• π‘’π‘’βˆ’π‘ π‘ π‘ π‘ π‘‘π‘‘π‘‘π‘‘βˆž 0 …….…………………………………………………………………………. (2.19) becomes: 𝐿𝐿 �𝑣𝑣 πœ•πœ•πœ•πœ• πœ•πœ•πœ•πœ• οΏ½ = 𝑣𝑣 πœ•πœ•πœ•πœ• πœ•πœ•πœ•πœ• ∫ 𝑐𝑐(𝑧𝑧, 𝑑𝑑)π‘’π‘’βˆ’π‘ π‘ π‘ π‘ βˆž 0 𝑑𝑑𝑑𝑑……………………………………………………………………….. (2.20) 𝐿𝐿 �𝑣𝑣 πœ•πœ•πœ•πœ• πœ•πœ•πœ•πœ• οΏ½ = 𝑣𝑣 πœ•πœ•πœ•πœ•Μ… πœ•πœ•πœ•πœ• ………………………………………………………………………………………………. cache/american_scientific_journal-3507.pdf txt/american_scientific_journal-3507.txt