Non-shrinking ModAB iteration (#861)

Author: DaniGlez

lib/BracketingNonlinearSolve/src/modAB.jl

@@ -66,6 +66,7 @@ function SciMLBase.__solve(
             end
         else # Anderson-Bjork method is used
             x3 = (x1 * y2 - y1 * x2) / (y2 - y1)
+            x3 = clamp(x3, nextfloat(x1), prevfloat(x2)) 
             y3 = f(x3)
             threshold /= 2
         end

lib/BracketingNonlinearSolve/test/rootfind_tests.jl

@@ -152,6 +152,20 @@ end
     end
 end
 
+@testitem "ModAB non-shrinking iteration" tags = [:core] begin
+    # Issue #860
+    a, b, c = 0.28299683548569865, 0.23110561490429102, -0.04293615418571393
+    f = (x, _) -> a * x^2 + b * x + c
+    tspan = (-18.26561304888476, -0.8216404439033063)
+
+    prob = IntervalNonlinearProblem{false}(f, tspan)
+    sol = solve(prob, ModAB(); abstol = 0.0, reltol = 0.0)
+
+    @test sol.retcode == ReturnCode.FloatingPointLimit
+    @test sol.left == -0.9726263117443217
+    @test sol.right == -0.9726263117443216
+end
+
 @testitem "Flipped Signs and Reversed Tspan" setup = [RootfindingTestSnippet] tags = [:core] begin
     @testset for alg in (
             Alefeld(), Bisection(), Brent(), Falsi(), ITP(), Muller(), Ridder(), ModAB(), nothing,