1 files changed, 16 insertions, 0 deletions
diff --git a/tutorials/module_3/3_7_Implicit_Method.md b/tutorials/module_3/3_7_Implicit_Method.md
new file mode 100644
index 0000000..04c71cf
--- /dev/null
+++ b/tutorials/module_3/3_7_Implicit_Method.md
@@ -0,0 +1,16 @@
+# Implicit Method
+Implicit methods for solving ODEs are another numerical schemes in which the new solution value at the next time step appears on both sides of the update equation. This makes them fundamentally different from explicit methods, where the next value is computed directly from already-known quantities. While explicit methods are simple and computationally cheap per step, implicit methods generally require solving algebraic equations at every step. In exchange, implicit methods provide much greater numerical stability, especially for stiff problems. The general idea of an implicit method for a first-order ODE is to write the time-stepping update in a form such that
+$$
+y_{n+1} = y_n + h f(t_{n+1}, y_{n+1})\tag{2}
+$$
+where $h$ is the step size. Unlike explicit schemes (where $f$ is evaluated at known values $t_n$, $y_n$), here the function is evaluated at the unknown point $t_{n+1}, y_{n+1}$. This results in an equation that must be solved for $y_{n+1}$ before advancing to the next step.
+
+Implicit methods are especially useful when dealing with stiff ODEs, where some components of the system change much faster than others. In such cases, explicit methods require extremely small time steps to remain stable, making them inefficient. Implicit schemes allow much larger time steps without losing stability, which makes them the preferred choice in fields like chemical kinetics, heat conduction, and structural dynamics with damping. Although they require more computational effort per step, they are often far more efficient overall for stiff problems.
+## Backwards Eulers
+The implicit counter part of Forward Euler is the Backward Euler method. Like Forward Euler, it advances the solution using a single slope estimate, but instead of using the slope at the current point, it uses the slope at the unknown future point. This creates an implicit update equation that must be solved at each step, making Backward Euler both the easiest implicit method to derive and an excellent starting point for studying implicit schemes.
+
+## Problem 1: Chemical Kinetics
+
+## Problem 2: 
+
+