Return InitialFailure from bracketing methods if not enclosing interval

src/bracketing/bisection.jl

@@ -39,6 +39,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Bisection,
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     i = 1
     if !iszero(fr)
         while i < maxiters

src/bracketing/brent.jl

@@ -26,6 +26,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Brent, args...;
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     if abs(fl) < abs(fr)
         c = right
         right = left

src/bracketing/falsi.jl

@@ -25,6 +25,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Falsi, args...;
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     # Regula Falsi Steps
     i = 0
     if !iszero(fr)

src/bracketing/itp.jl

@@ -75,6 +75,13 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::ITP, args...;
         return build_solution(
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
+
+    if sign(fl) == sign(fr)
+        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     ϵ = abstol
     #defining variables/cache
     k2 = alg.k2

src/bracketing/ridder.jl

@@ -25,6 +25,12 @@ function SciMLBase.solve(prob::IntervalNonlinearProblem, alg::Ridder, args...;
             prob, alg, right, fr; retcode = ReturnCode.ExactSolutionRight, left, right)
     end
 
+    if sign(fl) == sign(fr)
+        @warn "The interval is not an enclosing interval, opposite signs at the boundaries are required."
+        return build_solution(
+            prob, alg, left, fl; retcode = ReturnCode.InitialFailure, left, right)
+    end
+
     xo = oftype(left, Inf)
     i = 1
     if !iszero(fr)