198198 spatial_residual! (du, u, ss, 0.0 )
199199
200200 end
201- function jac_imp (J, u)
201+ function jac_imp (J, u)
202202 jacobian! (J, u, ss, 0.0 )
203203 end
204204
236236 0 (1 - γ)/ 2 γ 0 ;
237237 0 b1 b2 γ;]
238238 b_imp = [0 , b1, b2, γ]
239-
239+
240240
241241 n_stage = size (a_imp)[1 ] - 1
242242 K_exp = zeros (3 * N+ 1 , n_stage + 1 )
@@ -246,14 +246,14 @@ end
246246 u_stage = copy (u)
247247 for i_stage = 1 : n_stage
248248 f_exp (@view (K_exp[:, i_stage]), u_stage)
249- u_stage_temp = u + dt* (K_imp[:, 1 : i_stage- 1 ]* a_imp[i_stage+ 1 , 2 : i_stage]
249+ u_stage_temp = u + dt* (K_imp[:, 1 : i_stage- 1 ]* a_imp[i_stage+ 1 , 2 : i_stage]
250250 + K_exp[:, 1 : i_stage]* a_exp[i_stage+ 1 , 1 : i_stage])
251251
252252 K_imp[:, i_stage] = f_imp_solve (f_imp, jac_imp, u_stage_temp, dt* a_imp[i_stage+ 1 , i_stage+ 1 ])
253- u_stage = u_stage_temp + dt* K_imp[:, i_stage]* a_imp[i_stage+ 1 , i_stage+ 1 ]
253+ u_stage = u_stage_temp + dt* K_imp[:, i_stage]* a_imp[i_stage+ 1 , i_stage+ 1 ]
254254 end
255255 f_exp (@view (K_exp[:, n_stage+ 1 ]), u_stage)
256- u .+ = dt* (K_exp[:, 1 : n_stage+ 1 ]* b_exp[1 : n_stage+ 1 ] + K_imp[:, 1 : n_stage]* b_imp[2 : n_stage+ 1 ])
256+ u .+ = dt* (K_exp[:, 1 : n_stage+ 1 ]* b_exp[1 : n_stage+ 1 ] + K_imp[:, 1 : n_stage]* b_imp[2 : n_stage+ 1 ])
257257 end
258258 ref_ARS343 = norm (u)
259259 end
271271 ARS222 (NewtonsMethod (; max_iters = 1 )),
272272 ARS343 (NewtonsMethod (; max_iters = 1 )),
273273 )
274- reference_sol_norm = [860.2745315698107 ; 860.2745315698107 ; 860.4393569534262 ;
274+ reference_sol_norm = [860.2745315698107 ; 860.2745315698107 ; 860.4393569534262 ;
275275 860.452530117785 ; 860.452530117785 ; ref_ARS343]
276276
277277
289289 ),
290290 copy (u0),(0.0 , N_iter* dt), ss)
291291
292-
292+
293293 u = solve (single_column_prob_wfact_split , algo; dt= dt)
294294 @info norm (u. u[end ])
295295 @test norm (u. u[end ]) ≈ reference_sol_norm[i] atol = 1e3 eps ()
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