Newly modified method and its application to the coupled Boussinesq equation in ocean engineering with its linear stability analysis

Hajar Farhan Ismael,Hasan Bulut,Haci Mehmet Baskonus,Wei Gao

Table 1. Analytical and numerical solutions of v (x, t) for the equation (1 ) and its absolute errors when λ  = 3, μ  = 2, ε  = 0 under equation (13 ).

x i t i Exact solution Numerical solution Absolute error 0.01 0.1 0.9550303504 0.954955901 7.44484 × 10−5 0.02 0.1 0.9600213196 0.959960033 6.12866 × 10−5 0.03 0.1 0.9650142846 0.964966309 4.79749 × 10−5 0.04 0.1 0.9700089967 0.969974480 3.45162 × 10−5 0.05 0.1 0.9750052070 0.974984293 2.09135 × 10−5 0.06 0.1 0.9800026662 0.979995496 7.1697 × 10−6 0.07 0.1 0.9850011248 0.985007836 6.7119 × 10−6 0.08 0.1 0.9900003333 0.990021061 2.07283 × 10−5 0.09 0.1 0.9950000416 0.995034917 3.48762 × 10−5