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import streamlit as st
from PIL import Image
import pandas as pd
import numpy as np
import math
st.set_page_config(page_title="Numerical Methods Solver", layout="centered")
# Sidebar navigation
image = Image.open("src/ii.jpg")
st.sidebar.image(image, use_container_width=True)
# Sidebar navigation
st.sidebar.title("Navigation")
page = st.sidebar.radio("Go to", ["Overview", "Tutorial", "Solver"])
if page == "Overview":
st.image('src/okay-i-will-it.jpg', width = 600)
st.title("\U0001F4D8 Numerical Methods Solver")
st.markdown("""
#### 👋 Welcome!
This app helps you understand and solve **ordinary differential equations** (ODEs) using numerical methods.
---
#### 🔍 What You Can Do:
- Solve **ordinary differential equations (ODEs)** using methods like Euler, Runge-Kutta, Milne, and more
- Solve **systems of linear equations** using Gauss Elimination, Gauss-Jordan, Gauss-Seidel, Jacobi, and LU Decomposition
- Visualize **step-by-step calculations**
- Input your own function, step size, and initial conditions
- Get results up to 4–5 decimal places
---
#### 📌 Who Is This For?
- Students studying **Numerical Analysis** or **Linear Algebra**
- Educators who want a visual teaching tool
- Anyone learning how numerical methods work under the hood
---
#### 💡 Supported Methods (So Far)
**ODE Methods:**
- Euler's Method (Explicit)
- Euler's Method (Implicit)
- Heun’s Method (Improved Euler)
- Runge-Kutta 4th Order (RK4)
- Taylor Series Method (1st order)
- Milne's Predictor-Corrector Method
**Linear Algebraic Methods:**
- Gauss Elimination Method
- Gauss-Jordan Method
- Gauss-Seidel Iterative Method
- Jacobi Iteration Method
- LU Decomposition Method
---
#### 🧠 How It Works:
For ODEs:
- Provide a function of `x` and `y`
- Set initial values `x₀`, `y₀`, step size `h`, and number of steps `n`
For Linear Equations:
- Provide matrix `A` and vector `b` from your system of equations
The app will:
- Compute approximated values step by step
- Display intermediate and final results
""")
elif page == "Solver":
st.title("\U0001F9EE Numerical Methods Solver")
algebraic_methods = [
"Gauss Elimination Method",
"Gauss-Jordan Method",
"Gauss-Seidel Iterative Method",
"Jacobi Iteration Method",
"LU Decomposition Method"
]
ode_methods = [
"Euler (Explicit)",
"Euler (Implicit)",
"Heun’s Method (Improved Euler)",
"Runge-Kutta 4th Order (RK4)",
"Taylor Series Method",
"Milne's Predictor-Corrector Method"
]
method_type = st.radio("Choose a Method Category:", ["ODE Methods", "Algebraic Methods"])
if method_type == "ODE Methods":
method = st.selectbox("Choose a Numerical Method:", ode_methods)
col1, col2 = st.columns(2)
with col1:
x0 = st.number_input("Initial x (x₀):", value=0.0, format="%.5f")
h = st.number_input("Step size (h):", value=0.1, format="%.5f")
with col2:
f_str = st.text_input("Enter f(x, y):", "x + y")
y0 = st.number_input("Initial y (y₀):", value=1.0, format="%.5f")
n = st.number_input("Number of steps:", value=5, step=1)
st.markdown("### 🔄 Click below to solve")
compute = st.button("🔍 Compute Solution")
if compute:
try:
f = lambda x, y: eval(f_str, {"x": x, "y": y, "math": math})
x_vals = [x0]
y_vals = [y0]
x = x0
y = y0
results = [{"Step": 0, "x": round(x, 5), "y": round(y, 5)}]
if method == "Milne's Predictor-Corrector Method":
# Generate first 3 points using RK4
k1 = h * f(x, y)
k2 = h * f(x + h/2, y + k1/2)
k3 = h * f(x + h/2, y + k2/2)
k4 = h * f(x + h, y + k3)
y1 = y + (k1 + 2*k2 + 2*k3 + k4) / 6
x1 = x + h
k1 = h * f(x1, y1)
k2 = h * f(x1 + h/2, y1 + k1/2)
k3 = h * f(x1 + h/2, y1 + k2/2)
k4 = h * f(x1 + h, y1 + k3)
y2 = y1 + (k1 + 2*k2 + 2*k3 + k4) / 6
x2 = x1 + h
k1 = h * f(x2, y2)
k2 = h * f(x2 + h/2, y2 + k1/2)
k3 = h * f(x2 + h/2, y2 + k2/2)
k4 = h * f(x2 + h, y2 + k3)
y3 = y2 + (k1 + 2*k2 + 2*k3 + k4) / 6
x3 = x2 + h
xs = [x, x1, x2, x3]
ys = [y, y1, y2, y3]
results = [{"Step": i, "x": round(xs[i], 5), "y": round(ys[i], 5)} for i in range(4)]
for i in range(4, int(n) + 1):
f_n3 = f(xs[i-3], ys[i-3])
f_n2 = f(xs[i-2], ys[i-2])
f_n1 = f(xs[i-1], ys[i-1])
f_n = f(xs[i-0], ys[i-0])
# Predictor
y_pred = ys[i-4] + (4*h/3)*(2*f_n2 - f_n1 + 2*f_n)
x_new = xs[i-1] + h
# Corrector
f_pred = f(x_new, y_pred)
y_corr = ys[i-2] + (h/3)*(f_n1 + 4*f_n + f_pred)
xs.append(x_new)
ys.append(y_corr)
results.append({"Step": i, "x": round(x_new, 5), "y": round(y_corr, 5)})
else:
for i in range(1, int(n)+1):
if method == "Euler (Explicit)":
y = y + h * f(x, y)
x = x + h
elif method == "Euler (Implicit)":
y_new = y + h * f(x + h, y)
y = y_new
x = x + h
elif method == "Heun’s Method (Improved Euler)":
y_predict = y + h * f(x, y)
slope_avg = (f(x, y) + f(x + h, y_predict)) / 2
y = y + h * slope_avg
x = x + h
elif method == "Runge-Kutta 4th Order (RK4)":
k1 = h * f(x, y)
k2 = h * f(x + h/2, y + k1/2)
k3 = h * f(x + h/2, y + k2/2)
k4 = h * f(x + h, y + k3)
y += (k1 + 2*k2 + 2*k3 + k4) / 6
x += h
elif method == "Taylor Series Method":
y = y + h * f(x, y)
x = x + h
results.append({"Step": i, "x": round(x, 5), "y": round(y, 5)})
x_vals.append(x)
y_vals.append(y)
st.subheader(f"📊 Results using {method}")
df = pd.DataFrame(results)
st.dataframe(df)
except Exception as e:
st.error(f"⚠️ Error in function input: {e}")
elif method_type == "Algebraic Methods":
method = st.selectbox("Choose a Linear Algebra Method:", algebraic_methods)
st.write("Enter your coefficient matrix A and RHS vector b (1 equation per line).")
A_str = st.text_area("Enter matrix A (e.g., 2 1 -1\\n-3 -1 2\\n-2 1 2):", "2 1 -1\n-3 -1 2\n-2 1 2")
b_str = st.text_area("Enter vector b (e.g., 8\\n-11\\n-3):", "8\n-11\n-3")
if st.button("🔍 Solve System"):
try:
A = np.array([list(map(float, row.strip().split())) for row in A_str.strip().split('\n')])
b = np.array([float(num) for num in b_str.strip().split('\n')])
n = len(b)
if method == "Gauss Elimination Method":
for i in range(n):
for j in range(i + 1, n):
factor = A[j][i] / A[i][i]
A[j] = A[j] - factor * A[i]
b[j] = b[j] - factor * b[i]
x_sol = np.zeros(n)
for i in range(n - 1, -1, -1):
x_sol[i] = (b[i] - np.dot(A[i][i + 1:], x_sol[i + 1:])) / A[i][i]
elif method == "Gauss-Jordan Method":
aug = np.hstack((A, b.reshape(-1,1)))
for i in range(n):
aug[i] = aug[i] / aug[i][i]
for j in range(n):
if i != j:
aug[j] = aug[j] - aug[j][i] * aug[i]
x_sol = aug[:, -1]
elif method == "Gauss-Seidel Iterative Method":
x_sol = np.zeros(n)
for _ in range(25):
for i in range(n):
x_sol[i] = (b[i] - np.dot(A[i, :i], x_sol[:i]) - np.dot(A[i, i+1:], x_sol[i+1:])) / A[i, i]
elif method == "Jacobi Iteration Method":
x_sol = np.zeros(n)
for _ in range(25):
x_new = np.copy(x_sol)
for i in range(n):
x_new[i] = (b[i] - np.dot(A[i, :i], x_sol[:i]) - np.dot(A[i, i+1:], x_sol[i+1:])) / A[i, i]
x_sol = x_new
elif method == "LU Decomposition Method":
L = np.zeros_like(A)
U = np.zeros_like(A)
for i in range(n):
L[i][i] = 1
for j in range(i, n):
U[i][j] = A[i][j] - sum(L[i][k] * U[k][j] for k in range(i))
for j in range(i + 1, n):
L[j][i] = (A[j][i] - sum(L[j][k] * U[k][i] for k in range(i))) / U[i][i]
y = np.zeros(n)
for i in range(n):
y[i] = b[i] - np.dot(L[i, :i], y[:i])
x_sol = np.zeros(n)
for i in range(n - 1, -1, -1):
x_sol[i] = (y[i] - np.dot(U[i, i+1:], x_sol[i+1:])) / U[i][i]
df_result = pd.DataFrame({"Variable": [f"x{i + 1}" for i in range(n)], "Value": x_sol})
st.success("✅ System Solved Successfully")
st.dataframe(df_result)
except Exception as e:
st.error(f"⚠️ Error in matrix input: {e}")
elif page == "Tutorial":
st.title("📘 How to Use This Solver")
st.markdown("")
st.markdown("---")
st.markdown("")
st.markdown("### 🔢 ODE Methods Input")
st.markdown("""
These methods solve differential equations like dy/dx = f(x, y).
**Required Inputs:**
- `f(x, y)` — The function to solve (e.g., `x + y`, `x * y`, `math.exp(x)`)
- `Initial x₀` — Starting x-value (e.g., 0)
- `Initial y₀` — Starting y-value (e.g., 1)
- `Step size (h)` — E.g., 0.1
- `Number of steps (n)` — How many iterations (e.g., 5)
**Function Rules:**
- You can use basic operators: `+`, `-`, `*`, `/`, `**`
- You can use math functions like `math.sin(x)`, `math.exp(x)` — include `math.` prefix!
""")
st.markdown("")
st.markdown("---")
st.markdown("")
st.markdown("### 🧮 Algebraic Methods Input")
st.markdown("""
These methods solve systems like Ax = b.
**Required Inputs:**
- **Matrix A** — Coefficients of your equations
Example:
```
2 1 -1
-3 -1 2
-2 1 2
```
- **Vector b** — Right-hand side values
Example:
```
8
-11
-3
```
This represents:
```
2x₁ + 1x₂ - 1x₃ = 8
-3x₁ - 1x₂ + 2x₃ = -11
-2x₁ + 1x₂ + 2x₃ = -3
```
✅ Avoid extra spaces. Match the number of rows in A and b.
""")
st.markdown("---")
st.info("Make sure matrix A is square and matches vector b in dimensions for algebraic methods.")
st.success("You're all set! Head to the Solver tab to try it out.")
st.markdown("---")
st.markdown("<h8 style='text-align: LEFT; font-family:montserrat'>Numerical Method Solver built with ❤️ by Datapsalm</h8>", unsafe_allow_html=True)
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