Numerical Analysis: Numerical Methods for Differential Equations

This course gives you a solid foundation in numerical analysis of differential equations. You will learn how to construct, analyse, implement and apply numerical methods to solve initial value problems, boundary value problems, and various types of partial differential equations.

Topics covered include

• Time integration methods: Euler’s method, trapezoidal rule
• Multistep methods: Adams’ methods, Backward Differentiation Formulae (BDF)
• Explicit and implicit Runge-Kutta methods
• Error analysis, stability and convergence
• Stiff problems and A-stability, error control and adaptive step sizing
• Poisson’s equation: finite difference and finite element methods
• Elliptic, parabolic and hyperbolic PDEs
• Numerical schemes for time-dependent PDEs, including the diffusion equation
• Introduction to difference methods for conservation laws

The course is compulsory for the specialisation in Numerical Analysis within the Master’s Programme in Mathematics and is also offered as a standalone course.

You will learn through a mix of lectures and hands-on computer projects. The projects are mandatory and form a key part of the course, giving you practical experience in solving problems using numerical methods and programming.

Expect to work independently with computational tools, analyse results, and present your findings. The course encourages scientific thinking and problem-solving, with a strong focus on applying theory to real-world scenarios.

Assessment includes a written exam and project presentations. The grading scale is Fail, Pass, or Pass with Distinction.

This course prepares you for advanced studies and research in numerical analysis, scientific computing, and applied mathematics. It’s especially relevant if you aim to work in fields like engineering, physics, geoscience, or data-driven modelling.

You will gain skills that are valuable in both academia and industry, particularly in roles involving simulation, algorithm development, or computational problem-solving. The course also supports further studies within the Master's programme and related doctoral education.

Prerequisites

Admission to the course requires English 6/b and at least 90 credits of which at least 45 credits should be in mathematics and/or numerical analysis, including the courses NUMA01 Computational Programming with Python, 7.5 credits, MATB22 Linear Algebra 2, 7.5 credits, and MATB21 Analysis in Several Variables 1, 7,5 credits, or equivalent. In addition to these 45 credits, also one of the courses MATC12 Ordinary Differential Equations I, 7.5 credits, NUMA41 Numerical Analysis, Basic Course, 7.5 credits, and FYSB21 Physics: Mathematical Methods for Vibrations, Waves and Diffusion, 7.5 credits, or equivalent, is required.

Selection criteria

Seats are allocated according to: ECTS (HPAV): 100 %.

Tuition fees for non-EU/EEA citizens

Citizens of countries outside:

• The European Union (EU)
• The European Economic Area (EEA) and
• Switzerland

are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.

Tuition fees, payments and exemptions

Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125

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Note that you may also need to pay an application fee, or provide proof of exemption.

Application fee

No tuition fees for citizens of the EU, EEA and Switzerland

There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.