#NumericalMethods

√1001 − √1000 with 4 significant digits: 31.64 − 31.62 = 0.02. The true answer is 0.01581, so it's 26% off, with no mistakes. 🤯 Lecture 2 of our Numerical Methods series: how errors grow through + − × ÷, and how to fix cancellation. #Maths #NumericalMethods

How many solutions does eˣ = 3x have? Algebra can't say. Two curves can, in two seconds. 📈 Lecture 6 of our Numerical Methods series: the graphical method, plus how to count roots and spot the traps a table hides. #Maths #NumericalMethods

How many solutions does eˣ = 3x have? Algebra can't say. Two curves can, in two seconds. 📈 Lecture 6 of our Numerical Methods series: the graphical method, plus how to count roots and spot the traps a table hides. #Maths #NumericalMethods

√1001 − √1000 with 4 significant digits: 31.64 − 31.62 = 0.02. The true answer is 0.01581, so it's 26% off, with no mistakes. 🤯 Lecture 2 of our Numerical Methods series: how errors grow through + − × ÷, and how to fix cancellation. #Maths #NumericalMethods

Pendulum lab: L = 1.00 ± 0.01 m, T = 2.00 ± 0.01 s, so g = 9.87 ± what? 🤔 Lecture 4 of our Numerical Methods series: one formula for every error, then algebraic vs transcendental equations and how to trap a root. #Maths #NumericalMethods

f(2) = −1, f(3) = +16. Bisection guesses 2.5. Common sense says near 2, and the root is 2.0945. 🎯 Lecture 7 of our Numerical Methods series: regula falsi, the stuck endpoint, and the Illinois fix (7 steps instead of 16). #Maths #NumericalMethods

Root of x³ − x − 1 to 6 decimals: bisection needs 20 steps, regula falsi 16, Newton–Raphson 3. ⚡ The finale of our Numerical Methods series: tangents, quadratic convergence, when Newton fails, and every method compared. #Maths #NumericalMethods

A stock index lost half its value in 22 months, and nobody sold a single share. 📉 The culprit: chopping decimals. Lecture 1 of our Numerical Methods series covers round-off, truncation, significant digits and why 0.1 + 0.2 ≠ 0.3. #Maths #NumericalMethods

A pencil off by 1 cm: 10% error. A 1 km road off by 1 cm: 0.001%. Same error, very different story. 📏 Lecture 3 of our Numerical Methods series: absolute, relative and percentage errors, error bounds, and how to know when to stop iterating. #Maths #NumericalMethods

Guess a number from 1 to 1000. Always pick the middle and you'll have it in 10 guesses (2¹⁰ = 1024). 🎯 That game is the bisection method. Lecture 5 of our Numerical Methods series: 4 equations solved, and the step count known in advance. #Maths #NumericalMethods

Pendulum lab: L = 1.00 ± 0.01 m, T = 2.00 ± 0.01 s, so g = 9.87 ± what? 🤔 Lecture 4 of our Numerical Methods series: one formula for every error, then algebraic vs transcendental equations and how to trap a root. #Maths #NumericalMethods

It is a simple yet powerful hack to improve the convergence of Newton-Raphson iterations while using fewer load steps at the same time. #FEM #NumericalMethods #NonlinearFEM

Root of x³ − x − 1 to 6 decimals: bisection needs 20 steps, regula falsi 16, Newton–Raphson 3. ⚡ The finale of our Numerical Methods series: tangents, quadratic convergence, when Newton fails, and every method compared. #Maths #NumericalMethods

Guess a number from 1 to 1000. Always pick the middle and you'll have it in 10 guesses (2¹⁰ = 1024). 🎯 That game is the bisection method. Lecture 5 of our Numerical Methods series: 4 equations solved, and the step count known in advance. #Maths #NumericalMethods

f(2) = −1, f(3) = +16. Bisection guesses 2.5. Common sense says near 2, and the root is 2.0945. 🎯 Lecture 7 of our Numerical Methods series: regula falsi, the stuck endpoint, and the Illinois fix (7 steps instead of 16). #Maths #NumericalMethods

Eighty Years of the Finite Element Method: Birth, Evolution, and Future #openaccess @SpringerMath #NumericalMethods #Approximation #PDEs

This paper replaces expensive matrix-exponential calculations in Fokker-Planck equations with rational approximations, delivering similar accuracy while running 10-32× faster in benchmark tests. #NumericalMethods #ScientificComputing

🚀 Just built a Python-based Numerical Methods project! It implements numerical analysis and root-finding techniques for solving mathematical problems computationally. 🔗 #Python #NumericalMethods #NumericalAnalysis #Programming #GitHub #Coding

A new Special Issue opens for submission! Title: Symmetry in #NumericalMethods Editor: Dušan Nikezić and Nikola Mirkov Details: #callforpapers #mdpisymmetry #computationalfluiddynamics #timeseriesforecasting @Univerzitet_BG @ComSciMath_Mdpi

💡 New Special Issue Online! Title: Advances in #NumericalModeling Based on #GraphTheory Deadline: 30 April 2025 Submit via this link: #numericalmethods #simulation #optimization #MDPIOpenAccess @ComSciMath_Mdpi